Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000771
Mapping
Mp00176: Set partitions —rotate decreasing⟶ Set partitions
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => {{1}}
 => [1] => ([],1)
 => 1
{{1},{2}}
 => {{1},{2}}
 => [1,1] => ([(0,1)],2)
 => 1
{{1},{2,3}}
 => {{1,2},{3}}
 => [2,1] => ([(0,2),(1,2)],3)
 => 1
{{1},{2},{3}}
 => {{1},{2},{3}}
 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
{{1},{2,3,4}}
 => {{1,2,3},{4}}
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
{{1},{2,3},{4}}
 => {{1,2},{3},{4}}
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
{{1},{2,4},{3}}
 => {{1,3},{2},{4}}
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
{{1},{2},{3,4}}
 => {{1},{2,3},{4}}
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
{{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
{{1},{2,3,4,5}}
 => {{1,2,3,4},{5}}
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
{{1},{2,3,4},{5}}
 => {{1,2,3},{4},{5}}
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2,3,5},{4}}
 => {{1,2,4},{3},{5}}
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2,3},{4,5}}
 => {{1,2},{3,4},{5}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
{{1},{2,3},{4},{5}}
 => {{1,2},{3},{4},{5}}
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
{{1},{2,4,5},{3}}
 => {{1,3,4},{2},{5}}
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2,4},{3,5}}
 => {{1,3},{2,4},{5}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
{{1},{2,4},{3},{5}}
 => {{1,3},{2},{4},{5}}
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
{{1},{2,5},{3,4}}
 => {{1,4},{2,3},{5}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
{{1},{2},{3,4,5}}
 => {{1},{2,3,4},{5}}
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2},{3,4},{5}}
 => {{1},{2,3},{4},{5}}
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2,5},{3},{4}}
 => {{1,4},{2},{3},{5}}
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
{{1},{2},{3,5},{4}}
 => {{1},{2,4},{3},{5}}
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2},{3},{4,5}}
 => {{1},{2},{3,4},{5}}
 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2},{3},{4},{5}}
 => {{1},{2},{3},{4},{5}}
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
{{1},{2,3,4,5,6}}
 => {{1,2,3,4,5},{6}}
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
{{1},{2,3,4,5},{6}}
 => {{1,2,3,4},{5},{6}}
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3,4,6},{5}}
 => {{1,2,3,5},{4},{6}}
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3,4},{5,6}}
 => {{1,2,3},{4,5},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3,4},{5},{6}}
 => {{1,2,3},{4},{5},{6}}
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3,5,6},{4}}
 => {{1,2,4,5},{3},{6}}
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3,5},{4,6}}
 => {{1,2,4},{3,5},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3,5},{4},{6}}
 => {{1,2,4},{3},{5},{6}}
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3,6},{4,5}}
 => {{1,2,5},{3,4},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3},{4,5,6}}
 => {{1,2},{3,4,5},{6}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3},{4,5},{6}}
 => {{1,2},{3,4},{5},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3,6},{4},{5}}
 => {{1,2,5},{3},{4},{6}}
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3},{4,6},{5}}
 => {{1,2},{3,5},{4},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3},{4},{5,6}}
 => {{1,2},{3},{4,5},{6}}
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3},{4},{5},{6}}
 => {{1,2},{3},{4},{5},{6}}
 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
{{1},{2,4,5,6},{3}}
 => {{1,3,4,5},{2},{6}}
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,4,5},{3,6}}
 => {{1,3,4},{2,5},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4,5},{3},{6}}
 => {{1,3,4},{2},{5},{6}}
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,4,6},{3,5}}
 => {{1,3,5},{2,4},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4},{3,5,6}}
 => {{1,3},{2,4,5},{6}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4},{3,5},{6}}
 => {{1,3},{2,4},{5},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4,6},{3},{5}}
 => {{1,3,5},{2},{4},{6}}
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,4},{3,6},{5}}
 => {{1,3},{2,5},{4},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4},{3},{5,6}}
 => {{1,3},{2},{4,5},{6}}
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4},{3},{5},{6}}
 => {{1,3},{2},{4},{5},{6}}
 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
{{1},{2,5,6},{3,4}}
 => {{1,4,5},{2,3},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
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: St000774
Mapping
Mp00176: Set partitions —rotate decreasing⟶ Set partitions
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000774: Graphs ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => {{1}}
 => [1] => ([],1)
 => 1
{{1},{2}}
 => {{1},{2}}
 => [1,1] => ([(0,1)],2)
 => 1
{{1},{2,3}}
 => {{1,2},{3}}
 => [2,1] => ([(0,2),(1,2)],3)
 => 1
{{1},{2},{3}}
 => {{1},{2},{3}}
 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
{{1},{2,3,4}}
 => {{1,2,3},{4}}
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
{{1},{2,3},{4}}
 => {{1,2},{3},{4}}
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
{{1},{2,4},{3}}
 => {{1,3},{2},{4}}
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
{{1},{2},{3,4}}
 => {{1},{2,3},{4}}
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
{{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
{{1},{2,3,4,5}}
 => {{1,2,3,4},{5}}
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
{{1},{2,3,4},{5}}
 => {{1,2,3},{4},{5}}
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2,3,5},{4}}
 => {{1,2,4},{3},{5}}
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2,3},{4,5}}
 => {{1,2},{3,4},{5}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
{{1},{2,3},{4},{5}}
 => {{1,2},{3},{4},{5}}
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
{{1},{2,4,5},{3}}
 => {{1,3,4},{2},{5}}
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2,4},{3,5}}
 => {{1,3},{2,4},{5}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
{{1},{2,4},{3},{5}}
 => {{1,3},{2},{4},{5}}
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
{{1},{2,5},{3,4}}
 => {{1,4},{2,3},{5}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
{{1},{2},{3,4,5}}
 => {{1},{2,3,4},{5}}
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2},{3,4},{5}}
 => {{1},{2,3},{4},{5}}
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2,5},{3},{4}}
 => {{1,4},{2},{3},{5}}
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
{{1},{2},{3,5},{4}}
 => {{1},{2,4},{3},{5}}
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2},{3},{4,5}}
 => {{1},{2},{3,4},{5}}
 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2},{3},{4},{5}}
 => {{1},{2},{3},{4},{5}}
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
{{1},{2,3,4,5,6}}
 => {{1,2,3,4,5},{6}}
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
{{1},{2,3,4,5},{6}}
 => {{1,2,3,4},{5},{6}}
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3,4,6},{5}}
 => {{1,2,3,5},{4},{6}}
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3,4},{5,6}}
 => {{1,2,3},{4,5},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3,4},{5},{6}}
 => {{1,2,3},{4},{5},{6}}
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3,5,6},{4}}
 => {{1,2,4,5},{3},{6}}
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3,5},{4,6}}
 => {{1,2,4},{3,5},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3,5},{4},{6}}
 => {{1,2,4},{3},{5},{6}}
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3,6},{4,5}}
 => {{1,2,5},{3,4},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3},{4,5,6}}
 => {{1,2},{3,4,5},{6}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3},{4,5},{6}}
 => {{1,2},{3,4},{5},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3,6},{4},{5}}
 => {{1,2,5},{3},{4},{6}}
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,3},{4,6},{5}}
 => {{1,2},{3,5},{4},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3},{4},{5,6}}
 => {{1,2},{3},{4,5},{6}}
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,3},{4},{5},{6}}
 => {{1,2},{3},{4},{5},{6}}
 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
{{1},{2,4,5,6},{3}}
 => {{1,3,4,5},{2},{6}}
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,4,5},{3,6}}
 => {{1,3,4},{2,5},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4,5},{3},{6}}
 => {{1,3,4},{2},{5},{6}}
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,4,6},{3,5}}
 => {{1,3,5},{2,4},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4},{3,5,6}}
 => {{1,3},{2,4,5},{6}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4},{3,5},{6}}
 => {{1,3},{2,4},{5},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4,6},{3},{5}}
 => {{1,3,5},{2},{4},{6}}
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1},{2,4},{3,6},{5}}
 => {{1,3},{2,5},{4},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4},{3},{5,6}}
 => {{1,3},{2},{4,5},{6}}
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2,4},{3},{5},{6}}
 => {{1,3},{2},{4},{5},{6}}
 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
{{1},{2,5,6},{3,4}}
 => {{1,4,5},{2,3},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1},{2},{3},{4,5,6},{7}}
 => {{1},{2},{3,4,5},{6},{7}}
 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
{{1},{2},{3},{4,5,7},{6}}
 => {{1},{2},{3,4,6},{5},{7}}
 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
{{1},{2},{3},{4,6,7},{5}}
 => {{1},{2},{3,5,6},{4},{7}}
 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
Description
The maximal multiplicity of a Laplacian eigenvalue in a graph.