Identifier
Values
([(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(2,3)],4) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(1,3),(2,3)],4) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(1,2),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => 3
([(0,3),(1,2),(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(2,4),(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(1,4),(2,4),(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(1,4),(2,3)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(2,3),(2,4),(3,4)],5) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => 3
([(1,4),(2,3),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => 3
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(3,5),(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(2,5),(3,5),(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(2,5),(3,4)],6) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(1,2),(3,5),(4,5)],6) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(3,4),(3,5),(4,5)],6) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => 3
([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(1,5),(2,4),(3,4),(3,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
([(1,2),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,3),(2,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(4,2),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,5),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(2,4),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 3
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(2,4),(3,4),(4,5)],6) => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => 3
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(2,4),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => 3
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(2,4),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => 3
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => 3
([(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(3,6),(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(2,6),(3,6),(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(3,6),(4,5)],7) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(2,3),(4,6),(5,6)],7) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(4,5),(4,6),(5,6)],7) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => 3
([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(1,2),(3,6),(4,6),(5,6)],7) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => 2
([(3,5),(3,6),(4,5),(4,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
([(1,6),(2,6),(3,5),(4,5)],7) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
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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.
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.
Map
weak duplicate order
Description
The weak duplicate order of the de-duplicate of a graph.
Let $G=(V, E)$ be a graph and let $N=\{ N_v | v\in V\}$ be the set of (distinct) neighbourhoods of $G$.
This map yields the poset obtained by ordering $N$ by reverse inclusion.
Let $G=(V, E)$ be a graph and let $N=\{ N_v | v\in V\}$ be the set of (distinct) neighbourhoods of $G$.
This map yields the poset obtained by ordering $N$ by reverse inclusion.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
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