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.