# Automorphism

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Automorphismавтоморфизм (ор)графа.

1. For an undirected graph, see Isomorphic graphs.

2. For a directed graph, automorphism is a permutation $\,\alpha$ of $\,V(G)$ such that the number of $\,(x,y)$-edges is the same as the number of $(\,\alpha(x), \alpha(y))$-edges $(x,y \in V(G))$. We also speak of the automorphism of a graph $\,G$ with colored edges. This means a permutation $\,\alpha$ such that the number of $\,(x,y)$-edges is the same as the number of $(\,\alpha(x), \alpha(y))$-edges with any given color.

The set of all automorphisms of a (di)graph forms a permutation group $\,A(G)$.

## Литература

• Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.