- FindStat

Your data matches 11 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001846

Mapping

St001846: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

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

Description

The number of elements which do not have a complement in the lattice. A complement of an element $x$ in a lattice is an element $y$ such that the meet of $x$ and $y$ is the bottom element and their join is the top element.

Matching statistic: St000259

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%

Values

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

Description

The diameter of a connected graph. This is the greatest distance between any pair of vertices.

Matching statistic: St000260

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%

Values

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

Description

The radius of a connected graph. This is the minimum eccentricity of any vertex.

Matching statistic: St000302

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000302: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%

Values

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

Description

The determinant of the distance matrix of a connected graph.

Matching statistic: St000466

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000466: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%

Values

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

Description

The Gutman (or modified Schultz) index of a connected graph. This is $$\sum_{\{u,v\}\subseteq V} d(u)d(v)d(u,v)$$ where $d(u)$ is the degree of vertex $u$ and $d(u,v)$ is the distance between vertices $u$ and $v$. For trees on $n$ vertices, the modified Schultz index is related to the Wiener index via $S^\ast(T)=4W(T)-(n-1)(2n-1)$ [1].

Matching statistic: St000467

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000467: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%

Values

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

Description

The hyper-Wiener index of a connected graph. This is $$ \sum_{\{u,v\}\subseteq V} d(u,v)+d(u,v)^2. $$

Matching statistic: St000771

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%

Values

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

Description

The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $2$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore statistic $1$.

Matching statistic: St000772

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%

Values

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

Description

The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $1$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$. The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].

Matching statistic: St000777

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%

Values

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

Description

The number of distinct eigenvalues of the distance Laplacian of a connected graph.

Matching statistic: St001645

Mapping

Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%

Values

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

Description

The pebbling number of a connected graph.

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St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons.