- FindStat

Your data matches 13 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000906
(load all 3 compositions to match this statistic)

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00263: Lattices —join irreducibles⟶ Posets
St000906: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],4)
 => 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,1),(0,2),(0,3)],4)
 => 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(3,1),(3,2)],4)
 => 3
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,3),(1,3),(3,2)],4)
 => 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(1,2)],3)
 => 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],5)
 => 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],4)
 => 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => 2
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,1),(0,2),(0,3)],4)
 => 2
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 3
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 4
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 2
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(0,3),(3,1)],4)
 => 2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(4,1),(4,2),(4,3)],5)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => 3
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],2)
 => 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => 4
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(2,3)],4)
 => 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(1,2)],3)
 => 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(1,2)],3)
 => 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(1,2),(1,3)],4)
 => 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,1),(0,2)],3)
 => 2
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,1)],2)
 => 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3

Description

The length of the shortest maximal chain in a poset.

Matching statistic: St000553

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000553: Graphs ⟶ ℤResult quality: 76% ●values known / values provided: 76%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 3
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 3
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 5
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 2
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 3
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => 4
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
 => 3
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => 4
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 3
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2
([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 3
([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 4
([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3
([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ?
 => ? = 3
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 4
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ?
 => ? = 2
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ?
 => ? = 3
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ?
 => ? = 2
([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ?
 => ? = 4
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ?
 => ? = 2
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ?
 => ? = 1
([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ?
 => ? = 5
([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ?
 => ? = 4
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 2
([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ?
 => ? = 2
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ?
 => ? = 1
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 3
([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 5
([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ?
 => ? = 5
([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
 => ? = 5
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
 => ? = 1
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 5
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ?
 => ? = 2
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(7,1),(7,2),(7,3),(7,4),(7,6)],9)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ?
 => ? = 3
([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ?
 => ? = 4
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ?
 => ? = 2
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ?
 => ? = 3
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,8),(6,1),(6,2),(6,5),(8,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ?
 => ? = 2
([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,8),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)
 => ? = 2
([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ?
 => ? = 3
([(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(5,7),(6,3),(6,5),(7,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ?
 => ? = 2
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ?
 => ? = 3
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ?
 => ? = 4

Description

The number of blocks of a graph. A cut vertex is a vertex whose deletion increases the number of connected components. A block is a maximal connected subgraph which itself has no cut vertices. Two distinct blocks cannot overlap in more than a single cut vertex.

Matching statistic: St000552

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000552: Graphs ⟶ ℤResult quality: 76% ●values known / values provided: 76%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0 = 1 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 1 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3 = 4 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0 = 1 - 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 2 = 3 - 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 1 - 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 1 - 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => 0 = 1 - 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 4 = 5 - 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 1 - 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 1 = 2 - 1
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 1 = 2 - 1
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 2 = 3 - 1
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 1 - 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => 3 = 4 - 1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 1 = 2 - 1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0 = 1 - 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
 => 2 = 3 - 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 1 - 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => 3 = 4 - 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => 0 = 1 - 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 1 = 2 - 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0 = 1 - 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => 0 = 1 - 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => 0 = 1 - 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => 0 = 1 - 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1 - 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2 - 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 3 - 1
([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 4 - 1
([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2 - 1
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3 - 1
([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2 - 1
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ?
 => ? = 3 - 1
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 4 - 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ?
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ?
 => ? = 3 - 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ?
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ?
 => ? = 4 - 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ?
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ?
 => ? = 1 - 1
([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ?
 => ? = 5 - 1
([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ?
 => ? = 4 - 1
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3 - 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ?
 => ? = 1 - 1
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 3 - 1
([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 5 - 1
([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ?
 => ? = 5 - 1
([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
 => ? = 5 - 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
 => ? = 1 - 1
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 5 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ?
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1 - 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ?
 => ? = 2 - 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(7,1),(7,2),(7,3),(7,4),(7,6)],9)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2 - 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ?
 => ? = 3 - 1
([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ?
 => ? = 4 - 1
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ?
 => ? = 2 - 1
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ?
 => ? = 3 - 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,8),(6,1),(6,2),(6,5),(8,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2 - 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ?
 => ? = 2 - 1
([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,8),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)
 => ? = 2 - 1
([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ?
 => ? = 3 - 1
([(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(5,7),(6,3),(6,5),(7,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2 - 1
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ?
 => ? = 2 - 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3 - 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ?
 => ? = 3 - 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ?
 => ? = 4 - 1

Description

The number of cut vertices of a graph. A cut vertex is one whose deletion increases the number of connected components.

Matching statistic: St000723

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000723: Graphs ⟶ ℤResult quality: 76% ●values known / values provided: 76%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 6 = 5 + 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => 4 = 3 + 1
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(5,6)],7)
 => 5 = 4 + 1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => 3 = 2 + 1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => 4 = 3 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(3,6),(4,5)],7)
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(5,6)],7)
 => 5 = 4 + 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 3 + 1
([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 4 + 1
([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ?
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 4 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ?
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ?
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ?
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ?
 => ? = 4 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ?
 => ? = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ?
 => ? = 5 + 1
([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ?
 => ? = 4 + 1
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 1 + 1
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 3 + 1
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 2 + 1
([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ?
 => ? = 2 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 3 + 1
([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 5 + 1
([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ?
 => ? = 5 + 1
([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 5 + 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 + 1
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 5 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ?
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ?
 => ? = 2 + 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(7,1),(7,2),(7,3),(7,4),(7,6)],9)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2 + 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ?
 => ? = 3 + 1
([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ?
 => ? = 4 + 1
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ?
 => ? = 2 + 1
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ?
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,8),(6,1),(6,2),(6,5),(8,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ?
 => ? = 2 + 1
([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 2 + 1
([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ?
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(5,7),(6,3),(6,5),(7,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ?
 => ? = 2 + 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ?
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ?
 => ? = 4 + 1

Description

The maximal cardinality of a set of vertices with the same neighbourhood in a graph. The set of so called mating graphs, for which this statistic equals $1$, is enumerated by [1].

Matching statistic: St000986

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000986: Graphs ⟶ ℤResult quality: 76% ●values known / values provided: 76%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 6 = 5 + 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => 4 = 3 + 1
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(5,6)],7)
 => 5 = 4 + 1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => 3 = 2 + 1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => 4 = 3 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(3,6),(4,5)],7)
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(5,6)],7)
 => 5 = 4 + 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 3 + 1
([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 4 + 1
([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ?
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 4 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ?
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ?
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ?
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ?
 => ? = 4 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ?
 => ? = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ?
 => ? = 5 + 1
([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ?
 => ? = 4 + 1
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 1 + 1
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 3 + 1
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 2 + 1
([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ?
 => ? = 2 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 3 + 1
([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 5 + 1
([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ?
 => ? = 5 + 1
([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 5 + 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 + 1
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 5 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ?
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ?
 => ? = 2 + 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(7,1),(7,2),(7,3),(7,4),(7,6)],9)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2 + 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ?
 => ? = 3 + 1
([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ?
 => ? = 4 + 1
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ?
 => ? = 2 + 1
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ?
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,8),(6,1),(6,2),(6,5),(8,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ?
 => ? = 2 + 1
([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 2 + 1
([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ?
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(5,7),(6,3),(6,5),(7,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ?
 => ? = 2 + 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ?
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ?
 => ? = 4 + 1

Description

The multiplicity of the eigenvalue zero of the adjacency matrix of the graph.

Matching statistic: St001691

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001691: Graphs ⟶ ℤResult quality: 76% ●values known / values provided: 76%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 6 = 5 + 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => 4 = 3 + 1
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(5,6)],7)
 => 5 = 4 + 1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => 3 = 2 + 1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => 4 = 3 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(3,6),(4,5)],7)
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(5,6)],7)
 => 5 = 4 + 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 3 + 1
([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 4 + 1
([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ?
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 4 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ?
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ?
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ?
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ?
 => ? = 4 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ?
 => ? = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ?
 => ? = 5 + 1
([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ?
 => ? = 4 + 1
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 1 + 1
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 3 + 1
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 2 + 1
([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ?
 => ? = 2 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 3 + 1
([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 5 + 1
([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ?
 => ? = 5 + 1
([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 5 + 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 + 1
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 5 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ?
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)
 => ?
 => ? = 2 + 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(7,1),(7,2),(7,3),(7,4),(7,6)],9)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2 + 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ?
 => ? = 3 + 1
([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)
 => ?
 => ? = 4 + 1
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)
 => ?
 => ? = 2 + 1
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)
 => ?
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,8),(6,1),(6,2),(6,5),(8,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)
 => ?
 => ? = 2 + 1
([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 2 + 1
([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)
 => ?
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(5,7),(6,3),(6,5),(7,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)
 => ?
 => ? = 2 + 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
 => ?
 => ? = 3 + 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)
 => ?
 => ? = 4 + 1

Description

The number of kings in a graph. A vertex of a graph is a king, if all its neighbours have smaller degree. In particular, an isolated vertex is a king.

Matching statistic: St000907
(load all 4 compositions to match this statistic)

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000907: Posets ⟶ ℤResult quality: 68% ●values known / values provided: 68%●distinct values known / distinct values provided: 100%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 3 = 2 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => 3 = 2 + 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 3 = 2 + 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 4 = 3 + 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 4 = 3 + 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => 3 = 2 + 1
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ? = 3 + 1
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ? = 4 + 1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 3 = 2 + 1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 2 + 1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => 4 = 3 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ? = 4 + 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ? = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => 2 = 1 + 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 3 = 2 + 1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 4 = 3 + 1
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ? = 4 + 1
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 4 = 3 + 1
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 1 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ? = 2 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ? = 3 + 1
([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ? = 4 + 1
([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ? = 3 + 1
([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ? = 4 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ? = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ? = 4 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ? = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,7),(7,2)],8)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ? = 1 + 1
([(0,2),(0,3),(0,5),(1,6),(2,7),(3,7),(4,1),(5,4),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ? = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ? = 2 + 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ? = 3 + 1
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ? = 1 + 1
([(0,3),(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(7,5)],8)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ? = 3 + 1
([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ? = 5 + 1
([(0,2),(0,3),(0,5),(1,6),(2,7),(3,7),(4,1),(4,7),(5,4),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ? = 1 + 1
([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ? = 4 + 1
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ? = 3 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 1 + 1
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 3 + 1
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 2 + 1
([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)
 => ? = 2 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)
 => ? = 1 + 1
([(0,6),(1,7),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5),(7,4)],8)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ? = 3 + 1
([(0,5),(1,7),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4),(6,7)],8)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 2 + 1
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 3 + 1
([(0,5),(1,7),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 2 + 1
([(0,6),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4),(7,5)],8)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ? = 4 + 1
([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ? = 5 + 1
([(0,5),(1,7),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 2 + 1
([(0,4),(0,5),(1,7),(3,6),(4,3),(5,1),(5,6),(6,7),(7,2)],8)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
 => ? = 5 + 1
([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ? = 5 + 1
([(0,3),(0,5),(2,7),(3,6),(4,2),(5,4),(5,6),(6,7),(7,1)],8)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 2 + 1

Description

The number of maximal antichains of minimal length in a poset.

Matching statistic: St000315
(load all 5 compositions to match this statistic)

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000315: Graphs ⟶ ℤResult quality: 63% ●values known / values provided: 63%●distinct values known / distinct values provided: 83%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 6 = 5 + 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 1 + 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => ? = 3 + 1
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(5,6)],7)
 => ? = 4 + 1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? = 2 + 1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => ? = 3 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(3,6),(4,5)],7)
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(5,6)],7)
 => ? = 4 + 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(5,6)],7)
 => ? = 4 + 1
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => 4 = 3 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 2 = 1 + 1
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([],7)
 => ? = 6 + 1
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(5,6)],7)
 => ? = 4 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
 => ?
 => ? = 2 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5)],8)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,4),(7,6)],8)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 3 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
 => ?
 => ? = 4 + 1
([(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,3),(5,4),(6,7)],8)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 3 = 2 + 1
([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)
 => ?
 => ? = 2 + 1
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
 => ?
 => ? = 3 + 1
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 4 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ?
 => ? = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ?
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
 => ?
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
 => ?
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
 => ?
 => ? = 4 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)
 => ?
 => ? = 1 + 1
([(0,3),(0,4),(0,5),(0,6),(1,7),(3,7),(4,7),(5,7),(6,1),(7,2)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(3,6),(4,5)],7)
 => ? = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,7),(7,2)],8)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,2),(0,3),(0,5),(1,6),(2,7),(3,7),(4,1),(5,4),(5,7),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)
 => ?
 => ? = 2 + 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)
 => ?
 => ? = 1 + 1
([(0,3),(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(7,5)],8)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => ? = 3 + 1
([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
 => ?
 => ? = 5 + 1
([(0,2),(0,3),(0,5),(1,6),(2,7),(3,7),(4,1),(4,7),(5,4),(7,6)],8)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
 => ?
 => ? = 4 + 1
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 3 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 1 + 1
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 3 + 1
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 2 + 1
([(0,3),(0,5),(1,7),(2,7),(3,6),(4,2),(5,1),(5,4),(5,6),(6,7)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 1

Description

The number of isolated vertices of a graph.

Matching statistic: St000454

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 17%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 4 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 1 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 + 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 3 + 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 5 + 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 1 + 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 + 1
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3 + 1
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => ? = 4 + 1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 2 + 1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 1 + 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
 => ? = 3 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ? = 4 + 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 1 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 3 + 1
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ? = 4 + 1
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 1
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,6),(2,7),(3,5),(4,5),(4,7),(5,6),(7,1)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,4),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,3),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,2),(4,6),(5,1),(5,6),(6,3)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,7),(2,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(7,6)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,7),(2,7),(3,2),(3,6),(4,3),(5,1),(5,6),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,4)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,5),(5,1),(5,2),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,5),(0,6),(1,7),(2,7),(3,4),(4,2),(5,3),(6,1)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,5),(1,6),(2,6),(3,5),(4,1),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,4),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,8),(5,6),(6,7),(8,1),(8,6)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,7),(5,8),(7,2),(8,1)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,8),(2,6),(3,7),(4,6),(4,7),(5,1),(6,8),(7,5)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,7),(7,1),(7,8),(8,2)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,2),(6,7),(8,1),(8,6)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(0,5),(1,7),(2,7),(3,8),(4,6),(5,4),(6,1),(6,2),(7,8)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,7),(2,6),(3,6),(4,8),(5,1),(6,5),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(6,5),(7,8)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(6,5),(6,7),(7,2),(7,3)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,2),(7,3),(7,4)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,2),(5,3),(5,8),(6,7),(8,1)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,3),(5,6),(6,7),(8,1)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,5),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,8),(2,8),(3,6),(3,8),(4,6),(5,1),(5,2),(5,3),(6,7),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,4),(0,5),(1,6),(2,6),(3,7),(4,3),(5,1),(5,2),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(6,1),(6,2),(6,3),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1
([(0,3),(0,5),(1,6),(2,8),(3,7),(4,2),(4,6),(5,1),(5,4),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 1 + 1

Description

The largest eigenvalue of a graph if it is integral. If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree. This statistic is undefined if the largest eigenvalue of the graph is not integral.

Matching statistic: St000422

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000422: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 17%

Values

([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 1 + 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 4 + 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 3
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 1 + 3
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 1 + 3
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 + 3
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 3
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 3 + 3
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 3
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 + 3
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 3
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 5 + 3
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 3
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 1 + 3
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 1 + 3
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2 + 3
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 + 3
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 3
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3 + 3
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => ? = 4 + 3
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 3
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 2 + 3
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 1 + 3
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
 => ? = 3 + 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 + 3
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
 => ? = 3 + 3
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2 + 3
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ? = 4 + 3
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 3
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 1 + 3
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 + 3
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 1 + 3
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 3
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 2 + 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 3
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 1 + 3
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ? = 2 + 3
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 3
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 3 + 3
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ? = 2 + 3
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 3
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ? = 4 + 3
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 3
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 3
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1 + 3
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,3),(0,4),(1,6),(2,7),(3,5),(4,5),(4,7),(5,6),(7,1)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,4),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,3),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,2),(4,6),(5,1),(5,6),(6,3)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,7),(2,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(7,6)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,7),(2,7),(3,2),(3,6),(4,3),(5,1),(5,6),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,4)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,5),(5,1),(5,2),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,5),(0,6),(1,7),(2,7),(3,4),(4,2),(5,3),(6,1)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,3),(0,4),(1,5),(1,6),(2,6),(3,5),(4,1),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,4),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,8),(5,6),(6,7),(8,1),(8,6)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,7),(5,8),(7,2),(8,1)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,3),(0,4),(1,8),(2,6),(3,7),(4,6),(4,7),(5,1),(6,8),(7,5)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,7),(7,1),(7,8),(8,2)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,2),(6,7),(8,1),(8,6)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(0,5),(1,7),(2,7),(3,8),(4,6),(5,4),(6,1),(6,2),(7,8)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,3),(0,4),(1,7),(2,6),(3,6),(4,8),(5,1),(6,5),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,2),(0,3),(0,4),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(6,5),(7,8)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(6,5),(6,7),(7,2),(7,3)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,2),(7,3),(7,4)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,2),(5,3),(5,8),(6,7),(8,1)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,3),(5,6),(6,7),(8,1)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,5),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,8),(2,8),(3,6),(3,8),(4,6),(5,1),(5,2),(5,3),(6,7),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,4),(0,5),(1,6),(2,6),(3,7),(4,3),(5,1),(5,2),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(6,1),(6,2),(6,3),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3
([(0,3),(0,5),(1,6),(2,8),(3,7),(4,2),(4,6),(5,1),(5,4),(6,8),(8,7)],9)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 1 + 3

Description

The energy of a graph, if it is integral. The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3]. The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.

The following 3 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St001479The number of bridges of a graph. St001826The maximal number of leaves on a vertex of a graph. St001672The restrained domination number of a graph.