Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000469
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Mapping
St000469: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 2
([(0,1)],2)
 => 2
([],3)
 => 3
([(1,2)],3)
 => 2
([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => 3
([],4)
 => 4
([(2,3)],4)
 => 2
([(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2)],4)
 => 3
([(0,3),(1,2),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([],5)
 => 5
([(3,4)],5)
 => 3
([(2,4),(3,4)],5)
 => 2
([(1,4),(2,4),(3,4)],5)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
([(1,4),(2,3)],5)
 => 3
([(1,4),(2,3),(3,4)],5)
 => 2
([(0,1),(2,4),(3,4)],5)
 => 2
([(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => 3
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 3
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].