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Your data matches 203 different statistics following compositions of up to 3 maps.
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Matching statistic: St001719
(load all 8 compositions to match this statistic)
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001719: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => 1
([],3)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2)],3)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
([(0,2),(1,2)],3)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,2),(1,3)],4)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 1
([],5)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => 1
([(2,3),(2,4)],5)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => 1
Description
The number of shortest chains of small intervals from the bottom to the top in a lattice. An interval $[a, b]$ in a lattice is small if $b$ is a join of elements covering $a$.
Matching statistic: St001111
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001111: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 96%●distinct values known / distinct values provided: 67%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(1,6),(2,4),(5,3),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(2,4),(4,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
Description
The weak 2-dynamic chromatic number of a graph. A $k$-weak-dynamic coloring of a graph $G$ is a (non-proper) coloring of $G$ in such a way that each vertex $v$ sees at least $\min\{d(v), k\}$ colors in its neighborhood. The $k$-weak-dynamic number of a graph is the smallest number of colors needed to find an $k$-dynamic coloring. This statistic records the $2$-weak-dynamic number of a graph.
Matching statistic: St001112
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001112: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 96%●distinct values known / distinct values provided: 67%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(1,6),(2,4),(5,3),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(2,4),(4,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
Description
The 3-weak dynamic number of a graph. A $k$-weak-dynamic coloring of a graph $G$ is a (non-proper) coloring of $G$ in such a way that each vertex $v$ sees at least $\min\{d(v), k\}$ colors in its neighborhood. The $k$-weak-dynamic number of a graph is the smallest number of colors needed to find an $k$-dynamic coloring. This statistic records the $3$-weak-dynamic number of a graph.
Matching statistic: St001694
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001694: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 96%●distinct values known / distinct values provided: 67%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(1,6),(2,4),(5,3),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(2,4),(4,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
Description
The number of maximal dissociation sets in a graph.
Matching statistic: St001716
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001716: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 96%●distinct values known / distinct values provided: 67%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(1,6),(2,4),(5,3),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(2,4),(4,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
Description
The 1-improper chromatic number of a graph. This is the least number of colours in a vertex-colouring, such that each vertex has at most one neighbour with the same colour.
Matching statistic: St001774
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001774: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 96%●distinct values known / distinct values provided: 67%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(1,6),(2,4),(5,3),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(2,4),(4,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
Description
The degree of the minimal polynomial of the smallest eigenvalue of a graph.
Matching statistic: St001775
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001775: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 96%●distinct values known / distinct values provided: 67%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(1,6),(2,4),(5,3),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(2,4),(4,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
Description
The degree of the minimal polynomial of the largest eigenvalue of a graph.
Matching statistic: St001776
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001776: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 96%●distinct values known / distinct values provided: 67%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1
([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1
([(1,6),(2,4),(5,3),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,3),(2,4),(4,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2
Description
The degree of the minimal polynomial of the largest Laplacian eigenvalue of a graph.
Matching statistic: St001306
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001306: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 96%●distinct values known / distinct values provided: 67%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 0 = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2 - 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2 - 1
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1 - 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3 - 1
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3 - 1
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1 - 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3 - 1
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3 - 1
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(1,6),(2,4),(5,3),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,6),(1,3),(2,4),(4,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
Description
The number of induced paths on four vertices in a graph.
Matching statistic: St001350
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001350: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 96%●distinct values known / distinct values provided: 67%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 0 = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,5),(1,4),(4,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,5),(1,3),(4,2),(5,4)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,4),(1,5),(1,6),(5,3),(6,2)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2 - 1
([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 2 - 1
([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(1,6),(2,5),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1 - 1
([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3 - 1
([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,6),(1,3),(1,6),(2,4),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3 - 1
([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 1 - 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3 - 1
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 1 - 1
([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 3 - 1
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 1 - 1
([(1,6),(2,4),(5,3),(6,5)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
([(0,6),(1,3),(2,4),(4,5),(4,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 2 - 1
Description
Half of the Albertson index of a graph. This is $\frac{1}{2}\sum_{\{u,v\}\in E}|d(u)-d(v)|$, where $E$ is the set of edges and $d_v$ is the degree of vertex $v$, see [1]. In particular, this statistic vanishes on graphs whose components are all regular, see [2].
The following 193 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001723The differential of a graph. St001724The 2-packing differential of a graph. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St000447The number of pairs of vertices of a graph with distance 3. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001577The minimal number of edges to add or remove to make a graph a cograph. St001613The binary logarithm of the size of the center of a lattice. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001881The number of factors of a lattice as a Cartesian product of lattices. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001845The number of join irreducibles minus the rank of a lattice. St001621The number of atoms of a lattice. St000181The number of connected components of the Hasse diagram for the poset. St000908The length of the shortest maximal antichain in a poset. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001301The first Betti number of the order complex associated with the poset. St001396Number of triples of incomparable elements in a finite poset. St001964The interval resolution global dimension of a poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001890The maximum magnitude of the Möbius function of a poset. St000914The sum of the values of the Möbius function of a poset. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001645The pebbling number of a connected graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000302The determinant of the distance matrix of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St000455The second largest eigenvalue of a graph if it is integral. St001877Number of indecomposable injective modules with projective dimension 2. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001875The number of simple modules with projective dimension at most 1. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001118The acyclic chromatic index of a graph. St000655The length of the minimal rise of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St000379The number of Hamiltonian cycles in a graph. St001141The number of occurrences of hills of size 3 in a Dyck path. St000456The monochromatic index of a connected graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001060The distinguishing index of a graph. St001545The second Elser number of a connected graph. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St001501The dominant dimension of magnitude 1 Nakayama algebras. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St001462The number of factors of a standard tableaux under concatenation. St001256Number of simple reflexive modules that are 2-stable reflexive. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St001181Number of indecomposable injective modules with grade at least 3 in the corresponding Nakayama algebra. St001193The dimension of $Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra $A$ such that $eA$ is a minimal faithful projective-injective module. St001204Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001696The natural major index of a standard Young tableau. St001722The number of minimal chains with small intervals between a binary word and the top element. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001820The size of the image of the pop stack sorting operator. St001846The number of elements which do not have a complement in the lattice. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St000057The Shynar inversion number of a standard tableau. St001568The smallest positive integer that does not appear twice in the partition. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001732The number of peaks visible from the left. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001139The number of occurrences of hills of size 2 in a Dyck path. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St000659The number of rises of length at least 2 of a Dyck path. St000674The number of hills of a Dyck path. St001496The number of graphs with the same Laplacian spectrum as the given graph. St001307The number of induced stars on four vertices in a graph. St001498The normalised height of a Nakayama algebra with magnitude 1. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001159Number of simple modules with dominant dimension equal to the global dimension in the corresponding Nakayama algebra. St000335The difference of lower and upper interactions. St000968We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n−1}]$ by adding $c_0$ to $c_{n−1}$. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001481The minimal height of a peak of a Dyck path. St000951The dimension of $Ext^{1}(D(A),A)$ of the corresponding LNakayama algebra. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St000322The skewness of a graph. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001518The number of graphs with the same ordinary spectrum as the given graph. St001578The minimal number of edges to add or remove to make a graph a line graph. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000264The girth of a graph, which is not a tree. St000699The toughness times the least common multiple of 1,. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000464The Schultz index of a connected graph. St001289The vector space dimension of the n-fold tensor product of D(A), where n is maximal such that this n-fold tensor product is nonzero. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001274The number of indecomposable injective modules with projective dimension equal to two. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. St000266The number of spanning subgraphs of a graph with the same connected components. St000267The number of maximal spanning forests contained in a graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000775The multiplicity of the largest eigenvalue in a graph. St000785The number of distinct colouring schemes of a graph. St001272The number of graphs with the same degree sequence. St001316The domatic number of a graph. St001395The number of strictly unfriendly partitions of a graph. St001475The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,0). St001476The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,-1). St001546The number of monomials in the Tutte polynomial of a graph. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000323The minimal crossing number of a graph. St000351The determinant of the adjacency matrix of a graph. St000368The Altshuler-Steinberg determinant of a graph. St000370The genus of a graph. St000403The Szeged index minus the Wiener index of a graph. St000636The hull number of a graph. St000637The length of the longest cycle in a graph. St000671The maximin edge-connectivity for choosing a subgraph. St000948The chromatic discriminant of a graph. St001029The size of the core of a graph. St001069The coefficient of the monomial xy of the Tutte polynomial of the graph. St001109The number of proper colourings of a graph with as few colours as possible. St001119The length of a shortest maximal path in a graph. St001271The competition number of a graph. St001281The normalized isoperimetric number of a graph. St001305The number of induced cycles on four vertices in a graph. St001309The number of four-cliques in a graph. St001310The number of induced diamond graphs in a graph. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. St001323The independence gap of a graph. St001324The minimal number of occurrences of the chordal-pattern in a linear ordering of the vertices of the graph. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001326The minimal number of occurrences of the interval-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001329The minimal number of occurrences of the outerplanar pattern in a linear ordering of the vertices of the graph. St001331The size of the minimal feedback vertex set. St001334The minimal number of occurrences of the 3-colorable pattern in a linear ordering of the vertices of the graph. St001335The cardinality of a minimal cycle-isolating set of a graph. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001357The maximal degree of a regular spanning subgraph of a graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St001638The book thickness of a graph. St001654The monophonic hull number of a graph. St001689The number of celebrities in a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001736The total number of cycles in a graph. St001793The difference between the clique number and the chromatic number of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001795The binary logarithm of the evaluation of the Tutte polynomial of the graph at (x,y) equal to (-1,-1). St001796The absolute value of the quotient of the Tutte polynomial of the graph at (1,1) and (-1,-1). St001797The number of overfull subgraphs of a graph.