# Complete rotation

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Complete rotationполное вращение (орграфа).

Let $\,G = Cay(\Gamma,S)$ be a Cayley digraph with $\,|S| = d$. (See also Associated Cayley digraph).

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

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.