Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001060
Mapping
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[-,+,+] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
 => 2
[+,-,+] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
 => 2
[2,1,+] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
 => 2
[3,-,1] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
 => 2
[-,+,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[+,+,-,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[-,-,+,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[-,+,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[+,-,-,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[+,-,+,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[-,+,4,3] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[+,-,4,3] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[+,3,2,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[-,3,2,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[-,4,2,3] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[+,4,+,2] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[-,4,+,2] => [3,2,1,4] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
[+,4,-,2] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[-,4,-,2] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[2,1,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[2,1,-,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[2,1,+,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[2,1,4,3] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[2,3,1,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[2,4,1,3] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[2,4,-,1] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[3,1,2,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[3,+,1,+] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,-,1,+] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,-,1,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[3,-,4,1] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[4,1,+,2] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[4,1,-,2] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[4,-,1,3] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[4,+,+,1] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[4,-,+,1] => [3,1,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[4,+,-,1] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[4,-,-,1] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
 => 2
[4,3,1,2] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[4,3,2,1] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[-,+,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[+,-,+,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[+,+,-,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[+,+,+,-,+] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
[-,-,+,+,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 3
[-,+,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 3
[-,+,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 3
[-,+,+,+,-] => [2,3,4,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 3
Description
The distinguishing index of a graph. This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism. If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.