Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000718
Mapping
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000718: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => => [1] => ([],1)
 => 0
[1,2] => 0 => [2] => ([],2)
 => 0
[2,1] => 1 => [1,1] => ([(0,1)],2)
 => 2
[1,2,3] => 00 => [3] => ([],3)
 => 0
[1,3,2] => 01 => [2,1] => ([(0,2),(1,2)],3)
 => 3
[2,1,3] => 10 => [1,2] => ([(1,2)],3)
 => 2
[2,3,1] => 10 => [1,2] => ([(1,2)],3)
 => 2
[3,1,2] => 10 => [1,2] => ([(1,2)],3)
 => 2
[3,2,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[1,2,3,4] => 000 => [4] => ([],4)
 => 0
[1,2,4,3] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 4
[1,3,2,4] => 010 => [2,2] => ([(1,3),(2,3)],4)
 => 3
[1,3,4,2] => 010 => [2,2] => ([(1,3),(2,3)],4)
 => 3
[1,4,2,3] => 010 => [2,2] => ([(1,3),(2,3)],4)
 => 3
[1,4,3,2] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[2,1,3,4] => 100 => [1,3] => ([(2,3)],4)
 => 2
[2,1,4,3] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[2,3,1,4] => 100 => [1,3] => ([(2,3)],4)
 => 2
[2,3,4,1] => 100 => [1,3] => ([(2,3)],4)
 => 2
[2,4,1,3] => 100 => [1,3] => ([(2,3)],4)
 => 2
[2,4,3,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[3,1,2,4] => 100 => [1,3] => ([(2,3)],4)
 => 2
[3,1,4,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
[3,2,1,4] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
[3,2,4,1] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
[3,4,1,2] => 100 => [1,3] => ([(2,3)],4)
 => 2
[3,4,2,1] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
[4,1,2,3] => 100 => [1,3] => ([(2,3)],4)
 => 2
[4,1,3,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
[4,2,1,3] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
[4,2,3,1] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
[4,3,1,2] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[4,3,2,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[1,2,3,4,5] => 0000 => [5] => ([],5)
 => 0
[1,2,3,5,4] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 5
[1,2,4,3,5] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 4
[1,2,4,5,3] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 4
[1,2,5,3,4] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 4
[1,2,5,4,3] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,3,2,4,5] => 0100 => [2,3] => ([(2,4),(3,4)],5)
 => 3
[1,3,2,5,4] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,3,4,2,5] => 0100 => [2,3] => ([(2,4),(3,4)],5)
 => 3
[1,3,4,5,2] => 0100 => [2,3] => ([(2,4),(3,4)],5)
 => 3
[1,3,5,2,4] => 0100 => [2,3] => ([(2,4),(3,4)],5)
 => 3
[1,3,5,4,2] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,4,2,3,5] => 0100 => [2,3] => ([(2,4),(3,4)],5)
 => 3
[1,4,2,5,3] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,4,3,2,5] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,4,3,5,2] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,4,5,2,3] => 0100 => [2,3] => ([(2,4),(3,4)],5)
 => 3
Description
The largest Laplacian eigenvalue of a graph if it is integral. This statistic is undefined if the largest Laplacian eigenvalue of the graph is not integral. Various results are collected in Section 3.9 of [1]