Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000777
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Mapping
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00250: Graphs —clique graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
 => ([],1)
 => ([],1)
 => 1
[1,2] => ([],2)
 => ([],2)
 => ([(0,1)],2)
 => 2
[2,1] => ([(0,1)],2)
 => ([],1)
 => ([],1)
 => 1
[1,2,3] => ([],3)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,3,2] => ([(1,2)],3)
 => ([],2)
 => ([(0,1)],2)
 => 2
[2,1,3] => ([(1,2)],3)
 => ([],2)
 => ([(0,1)],2)
 => 2
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => 1
[1,2,3,4] => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[1,2,4,3] => ([(2,3)],4)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,3,2,4] => ([(2,3)],4)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([(0,1)],2)
 => 2
[2,1,3,4] => ([(2,3)],4)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
[2,1,4,3] => ([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => 2
[2,3,1,4] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[3,1,2,4] => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([(0,1)],2)
 => 2
[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => 1
[1,2,3,4,5] => ([],5)
 => ([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,2,3,5,4] => ([(3,4)],5)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[1,2,4,3,5] => ([(3,4)],5)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,3,2,4,5] => ([(3,4)],5)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,3,4,2,5] => ([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 3
[1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 4
[1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 3
[1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,1)],2)
 => 2
[2,1,3,4,5] => ([(3,4)],5)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[2,1,3,5,4] => ([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
[2,1,4,3,5] => ([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
[2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3
[2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,1)],2)
 => 2
[2,3,1,4,5] => ([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.