Associated Cayley digraph

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Associated Cayley digraphсоотнесённый орграф Кэли.

Let \,\Gamma be a group and \,S be a generating set of \,\Gamma such that

(1) e \not \in S, \,e is the identity in \,\Gamma,

(2) s \in S \Leftrightarrow s^{-1} \in S.

The associated Cayley digraph \,Cay(\Gamma,S) is a digraph whose vertices are the elements of \,\Gamma and arcs are the couples \,(x,sx) for x \in \Gamma and s \in S.

With this definition, \,Cay(\Gamma,S) is a connected symmetric digraph (in fact, a strongly connected digraph).


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