Automorphism group of a graph

This article defines a natural context where a group occurs, or is associated, with another algebraic, topological, analytic or discrete structure
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Definition

Let $G$ be a graph with vertex set $V$, edge set $E$.

An automorphism of the graph $G$ is a bijection $\sigma :V\to V$ such that if $x,y\in V$ are connected (that is, $xy\in E$, then we have $\sigma (x)\sigma (y)\in E$.

The set of all automorphisms of a graph form a group under composition, called the automorphism group of the graph.