Identifier
Values
0 => ([(0,1)],2) => ([],2) => 2
1 => ([(0,1)],2) => ([],2) => 2
00 => ([(0,2),(2,1)],3) => ([],3) => 3
01 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 2
10 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 2
11 => ([(0,2),(2,1)],3) => ([],3) => 3
000 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 4
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 3
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 3
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
111 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 4
0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 5
1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 5
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 6
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 6
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 7
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 7
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Description
The distinguishing number of a graph.
This is the minimal number of colours needed to colour the vertices of a graph, such that only the trivial automorphism of the graph preserves the colouring.
For connected graphs, this statistic is at most one plus the maximal degree of the graph, with equality attained for complete graphs, complete bipartite graphs and the cycle with five vertices, see Theorem 4.2 of [2].
Map
incomparability graph
Description
The incomparability graph of a poset.
Map
poset of factors
Description
The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.