Complete rotation

Complete rotation --- полное вращение [орграфа].

Let [math]\displaystyle{ G = Cay(\Gamma,S) }[/math] be a Cayley digraph with [math]\displaystyle{ |S| = d }[/math]. (See also Associated Cayley digraph).

A complete rotation of [math]\displaystyle{ G }[/math] is a group automorphism [math]\displaystyle{ \omega }[/math] of [math]\displaystyle{ \Gamma }[/math] such that for some ordering [math]\displaystyle{ s_{0}, s_{1}, \ldots, s_{d-1} }[/math] of the elements of [math]\displaystyle{ S }[/math], we have [math]\displaystyle{ \omega(s_{i}) = s_{i+1} }[/math] for every [math]\displaystyle{ t \in Z }[/math].

Clearly, a rotation is a graph automorphism. A Cayley digraph with a complete rotation is called a rotational Cayley digraph.