Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000772
Mapping
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1] => [1] => ([],1)
 => 1
[1,0,1,0]
 => [2,1] => [2,1] => ([(0,1)],2)
 => 1
[1,0,1,0,1,0]
 => [3,2,1] => [2,3,1] => ([(0,2),(1,2)],3)
 => 1
[1,0,1,1,0,0]
 => [2,3,1] => [3,1,2] => ([(0,2),(1,2)],3)
 => 1
[1,1,0,0,1,0]
 => [3,1,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,0,1,0,1,0,1,0]
 => [4,3,2,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[1,0,1,0,1,1,0,0]
 => [3,4,2,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[1,0,1,1,0,0,1,0]
 => [4,2,3,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[1,0,1,1,0,1,0,0]
 => [3,2,4,1] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1
[1,0,1,1,1,0,0,0]
 => [2,3,4,1] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 2
[1,1,0,0,1,0,1,0]
 => [4,3,1,2] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[1,1,0,0,1,1,0,0]
 => [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 1
[1,1,0,1,0,0,1,0]
 => [4,2,1,3] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[1,1,1,0,0,0,1,0]
 => [4,1,2,3] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1
[1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,4,1] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1
[1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => [5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
[1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
[1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => [3,5,2,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
[1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,1,0,0,1,1,0,1,0,0]
 => [4,3,5,1,2] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
[1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,3] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,0,1,0,0,1,1,0,0]
 => [4,5,2,1,3] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,4] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1
[1,1,0,1,1,0,0,0,1,0]
 => [5,2,3,1,4] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => [4,2,5,3,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => [5,3,1,4,2] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,0,0,1,0,0,1,0]
 => [5,3,1,2,4] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,0,1,0,0,0,1,0]
 => [5,2,1,3,4] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [6,5,4,3,2,1] => [4,3,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [5,6,4,3,2,1] => [4,3,6,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [6,4,5,3,2,1] => [5,2,4,3,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [5,4,6,3,2,1] => [6,1,5,2,4,3] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [4,5,6,3,2,1] => [5,2,6,1,4,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [6,5,3,4,2,1] => [3,4,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [5,6,3,4,2,1] => [3,4,6,1,5,2] => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [6,4,3,5,2,1] => [3,5,2,4,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 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: St000264
(load all 2 compositions to match this statistic)
Mapping
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 17%
Values
[1,0]
 => [1,1,0,0]
 => [1,2] => ([],2)
 => ? = 1 + 3
[1,0,1,0]
 => [1,1,0,1,0,0]
 => [1,3,2] => ([(1,2)],3)
 => ? = 1 + 3
[1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [1,3,2,4] => ([(2,3)],4)
 => ? = 1 + 3
[1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 3
[1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 2 + 3
[1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ? = 1 + 3
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
 => ? = 1 + 3
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 2 + 3
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,3,4,2,5] => ([(2,4),(3,4)],5)
 => ? = 1 + 3
[1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2 + 3
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
 => ? = 1 + 3
[1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4 = 1 + 3
[1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? = 3 + 3
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,3,2,5,4,6] => ([(2,5),(3,4)],6)
 => ? = 1 + 3
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,3,5,2,4,6] => ([(2,5),(3,4),(4,5)],6)
 => ? = 1 + 3
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ? = 1 + 3
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 4 = 1 + 3
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,3,2,6,4,5] => ([(1,2),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,3,2,4,6,5] => ([(2,5),(3,4)],6)
 => ? = 2 + 3
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 2 + 3
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,3,2,4,5,6] => ([(4,5)],6)
 => ? = 3 + 3
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,3,4,2,5,6] => ([(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 3
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,4,2,5,3,6] => ([(2,5),(3,4),(4,5)],6)
 => ? = 1 + 3
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 4 = 1 + 3
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 2 + 3
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 4 = 1 + 3
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4 = 1 + 3
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ? = 1 + 3
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 4 = 1 + 3
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,4,2,3,6,5] => ([(1,2),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,4,2,3,5,6] => ([(3,5),(4,5)],6)
 => ? = 2 + 3
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 4 = 1 + 3
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4 = 1 + 3
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 3
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,5,2,3,4,6] => ([(2,5),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 4 + 3
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,3,2,5,4,7,6] => ([(1,6),(2,5),(3,4)],7)
 => ? = 1 + 3
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [1,3,5,2,4,7,6] => ([(1,2),(3,6),(4,5),(5,6)],7)
 => ? = 1 + 3
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
 => [1,3,2,5,7,4,6] => ([(1,2),(3,6),(4,5),(5,6)],7)
 => ? = 1 + 3
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [1,3,5,2,7,4,6] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ? = 1 + 3
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => [1,3,5,7,2,4,6] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
 => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7)
 => ? = 1 + 3
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
 => [1,3,5,2,4,6,7] => ([(3,6),(4,5),(5,6)],7)
 => ? = 1 + 3
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [1,3,2,5,6,4,7] => ([(2,3),(4,6),(5,6)],7)
 => ? = 1 + 3
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [1,3,5,2,6,4,7] => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ? = 1 + 3
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
 => [1,3,5,6,2,4,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
 => [1,3,2,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7)
 => ? = 1 + 3
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
 => [1,3,5,2,6,7,4] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ? = 1 + 3
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
 => [1,3,5,6,2,7,4] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [1,3,5,6,7,2,4] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
 => [1,3,2,6,4,7,5] => ([(1,2),(3,6),(4,5),(5,6)],7)
 => ? = 1 + 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,0,1,1,0,0,0]
 => [1,3,6,2,4,7,5] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ? = 1 + 3
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
 => [1,3,2,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
 => [1,3,6,2,7,4,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
 => [1,3,6,7,2,4,5] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,1,0,0]
 => [1,3,2,6,4,5,7] => ([(2,3),(4,6),(5,6)],7)
 => ? = 1 + 3
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
 => [1,3,6,2,4,5,7] => ([(2,6),(3,6),(4,5),(5,6)],7)
 => ? = 1 + 3
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
 => [1,3,2,4,6,5,7] => ([(3,6),(4,5)],7)
 => ? = 2 + 3
[1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => [1,3,4,2,6,5,7] => ([(2,3),(4,6),(5,6)],7)
 => ? = 1 + 3
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [1,3,4,6,7,2,5] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
 => [1,4,5,2,3,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,1,0,0,0]
 => [1,4,5,2,7,3,6] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
 => [1,4,5,7,2,3,6] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
 => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,0,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,1,0,0,0]
 => [1,4,5,2,6,3,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,0,0,1,1,0,1,1,0,0,0]
 => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
 => [1,4,5,6,2,3,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,0,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,1,1,0,0,1,0,0,0]
 => [1,4,5,2,6,7,3] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,1,0,0,0,0]
 => [1,4,5,6,2,7,3] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [1,4,5,6,7,2,3] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,1,0,0,0]
 => [1,4,6,2,3,7,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,1,0,0,1,0,0]
 => [1,4,2,6,7,3,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,1,0,0,0]
 => [1,4,6,2,7,3,5] => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => 4 = 1 + 3
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,1,1,1,0,0,0,0]
 => [1,4,6,7,2,3,5] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,1,0,0,0]
 => [1,4,6,2,3,5,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,0,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,1,0,0,0,1,1,0,0,0]
 => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => [1,5,2,6,3,7,4] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,0,1,1,0,0,0]
 => [1,5,6,2,3,7,4] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,1,0,0]
 => [1,5,2,6,7,3,4] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,1,0,0,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,1,0,0,0]
 => [1,5,6,2,7,3,4] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => 4 = 1 + 3
[1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,1,0,0]
 => [1,5,2,6,3,4,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
[1,1,1,0,0,1,0,0,1,1,0,0]
 => [1,1,1,1,0,0,1,0,0,1,1,0,0,0]
 => [1,5,6,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,1,0,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => [1,5,2,7,3,4,6] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,1,0,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,0,1,1,0,0,0]
 => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
 => [1,6,2,7,3,4,5] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 4 = 1 + 3
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,0]
 => [1,6,2,3,7,4,5] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 1 + 3
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.