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.

Литература

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