Your data matches 12 different statistics following compositions of up to 3 maps.
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Matching statistic: St001394
(load all 8 compositions to match this statistic)
Mapping
St001394: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 0
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 0
[1,3,2,4] => 0
[1,3,4,2] => 0
[1,4,2,3] => 1
[1,4,3,2] => 0
[2,1,3,4] => 0
[2,1,4,3] => 0
[2,3,1,4] => 0
[2,3,4,1] => 0
[2,4,1,3] => 1
[2,4,3,1] => 0
[3,1,2,4] => 1
[3,1,4,2] => 1
[3,2,1,4] => 0
[3,2,4,1] => 0
[3,4,1,2] => 1
[3,4,2,1] => 1
[4,1,2,3] => 1
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 0
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 0
[1,2,3,5,4] => 0
[1,2,4,3,5] => 0
[1,2,4,5,3] => 0
[1,2,5,3,4] => 1
[1,2,5,4,3] => 0
[1,3,2,4,5] => 0
[1,3,2,5,4] => 0
[1,3,4,2,5] => 0
[1,3,4,5,2] => 0
[1,3,5,2,4] => 1
[1,3,5,4,2] => 0
[1,4,2,3,5] => 1
[1,4,2,5,3] => 1
[1,4,3,2,5] => 0
[1,4,3,5,2] => 0
[1,4,5,2,3] => 1
Description
The genus of a permutation. The genus $g(\pi)$ of a permutation $\pi\in\mathfrak S_n$ is defined via the relation $$ n+1-2g(\pi) = z(\pi) + z(\pi^{-1} \zeta ), $$ where $\zeta = (1,2,\dots,n)$ is the long cycle and $z(\cdot)$ is the number of cycles in the permutation.
Matching statistic: St000259
Mapping
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 17%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 0
[1,2] => [1,2] => ([],2)
 => ([],1)
 => 0
[2,1] => [1,2] => ([],2)
 => ([],1)
 => 0
[1,2,3] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[1,3,2] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[2,1,3] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[2,3,1] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[3,1,2] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 1
[3,2,1] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,2,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,3,2,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,3,4,2] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[2,1,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,1,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,3,1,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,3,4,1] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000260
Mapping
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 17%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 0
[1,2] => [1,2] => ([],2)
 => ([],1)
 => 0
[2,1] => [1,2] => ([],2)
 => ([],1)
 => 0
[1,2,3] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[1,3,2] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[2,1,3] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[2,3,1] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[3,1,2] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 1
[3,2,1] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,2,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,3,2,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,3,4,2] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[2,1,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,1,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,3,1,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,3,4,1] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000302
Mapping
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000302: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 17%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 0
[1,2] => [1,2] => ([],2)
 => ([],1)
 => 0
[2,1] => [1,2] => ([],2)
 => ([],1)
 => 0
[1,2,3] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[1,3,2] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[2,1,3] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[2,3,1] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[3,1,2] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 1
[3,2,1] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,2,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,3,2,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,3,4,2] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[2,1,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,1,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,3,1,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,3,4,1] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
Description
The determinant of the distance matrix of a connected graph.
Matching statistic: St000466
Mapping
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000466: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 17%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 0
[1,2] => [1,2] => ([],2)
 => ([],1)
 => 0
[2,1] => [1,2] => ([],2)
 => ([],1)
 => 0
[1,2,3] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[1,3,2] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[2,1,3] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[2,3,1] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[3,1,2] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 1
[3,2,1] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,2,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,3,2,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,3,4,2] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[2,1,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,1,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,3,1,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,3,4,1] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
Description
The Gutman (or modified Schultz) index of a connected graph. This is $$\sum_{\{u,v\}\subseteq V} d(u)d(v)d(u,v)$$ where $d(u)$ is the degree of vertex $u$ and $d(u,v)$ is the distance between vertices $u$ and $v$. For trees on $n$ vertices, the modified Schultz index is related to the Wiener index via $S^\ast(T)=4W(T)-(n-1)(2n-1)$ [1].
Matching statistic: St000467
Mapping
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000467: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 17%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 0
[1,2] => [1,2] => ([],2)
 => ([],1)
 => 0
[2,1] => [1,2] => ([],2)
 => ([],1)
 => 0
[1,2,3] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[1,3,2] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[2,1,3] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[2,3,1] => [1,2,3] => ([],3)
 => ([],1)
 => 0
[3,1,2] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 1
[3,2,1] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,2,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,3,2,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,3,4,2] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[2,1,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,1,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,3,1,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,3,4,1] => [1,2,3,4] => ([],4)
 => ([],1)
 => 0
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 0
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 0
Description
The hyper-Wiener index of a connected graph. This is $$ \sum_{\{u,v\}\subseteq V} d(u,v)+d(u,v)^2. $$
Matching statistic: St000771
Mapping
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 17%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 1 = 0 + 1
[1,2] => [1,2] => ([],2)
 => ([],1)
 => 1 = 0 + 1
[2,1] => [1,2] => ([],2)
 => ([],1)
 => 1 = 0 + 1
[1,2,3] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[1,3,2] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[2,1,3] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[2,3,1] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[3,1,2] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,2,1] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,1,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,3,1,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,1] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
Description
The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $2$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore statistic $1$.
Matching statistic: St000772
Mapping
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 17%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 1 = 0 + 1
[1,2] => [1,2] => ([],2)
 => ([],1)
 => 1 = 0 + 1
[2,1] => [1,2] => ([],2)
 => ([],1)
 => 1 = 0 + 1
[1,2,3] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[1,3,2] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[2,1,3] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[2,3,1] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[3,1,2] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,2,1] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,1,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,3,1,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,1] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
Description
The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $1$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$. The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].
Matching statistic: St000777
Mapping
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 17%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 1 = 0 + 1
[1,2] => [1,2] => ([],2)
 => ([],1)
 => 1 = 0 + 1
[2,1] => [1,2] => ([],2)
 => ([],1)
 => 1 = 0 + 1
[1,2,3] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[1,3,2] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[2,1,3] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[2,3,1] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[3,1,2] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,2,1] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,1,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,3,1,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,1] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St001645
Mapping
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 17%
Values
[1] => [1] => ([],1)
 => ([],1)
 => 1 = 0 + 1
[1,2] => [1,2] => ([],2)
 => ([],1)
 => 1 = 0 + 1
[2,1] => [1,2] => ([],2)
 => ([],1)
 => 1 = 0 + 1
[1,2,3] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[1,3,2] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[2,1,3] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[2,3,1] => [1,2,3] => ([],3)
 => ([],1)
 => 1 = 0 + 1
[3,1,2] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,2,1] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,1,3,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,3] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,3,1,4] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,1] => [1,2,3,4] => ([],4)
 => ([],1)
 => 1 = 0 + 1
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 + 1
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
 => ([],1)
 => 1 = 0 + 1
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1 + 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 + 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 0 + 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
 => ([],1)
 => 1 = 0 + 1
Description
The pebbling number of a connected graph.
The following 2 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001330The hat guessing number of a graph. St001875The number of simple modules with projective dimension at most 1.