Associated Cayley digraph

Associated Cayley digraph --- соотнесённый орграф Кэли.

Let [math]\displaystyle{ \Gamma }[/math] be a group and [math]\displaystyle{ S }[/math] be a generating set of [math]\displaystyle{ \Gamma }[/math] such that

(1) [math]\displaystyle{ e \not \in S }[/math], [math]\displaystyle{ e }[/math] is the identity in [math]\displaystyle{ \Gamma }[/math],

(2) [math]\displaystyle{ s \in S \Leftrightarrow s^{-1} \in S }[/math].

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

With this definition, [math]\displaystyle{ Cay(\Gamma,S) }[/math] is a connected symmetric digraph (in fact, a strongly connected digraph).