An $\textdef{automorphism of a graph}$ is a permutation $\sigma$ of the set of vertices such that two vertices $x$ and $y$ form an edge if and only if $\sigma(x)$ and $\sigma(y)$ form an edge. The $\textdef{automorphism group of a graph}$ is the set of all automorphisms of the graph. If $\mathcal{G}$ is a graph, its automorphism group is denoted $\aut(\mathcal{G})$.

• None.

definition.automorphism_of_a_graph.tex

%%%%%
% DEPENDENCIES 
% RequiredMacros: \DeclareMathOperator{\aut}{Aut} 
%%%%%
An \textdef{automorphism of a graph} is a permutation $\sigma$ of the set of vertices such that two vertices $x$ and $y$ form an edge if and only if $\sigma(x)$ and $\sigma(y)$ form an edge. The  \textdef{automorphism group of a graph} is the set of all automorphisms of the graph. If $\mathcal{G}$ is a graph, its automorphism group is denoted $\aut(\mathcal{G})$.

• Graph automorphism

definition needsreview rjosh