# 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).

## Литература

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