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====== Automorphism Of A Graph ======
====Definition==== 
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 $\aut(\mathcal{G})$.


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==== Remarks ==== 
  * None.


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==== $\LaTeX$ version ====
<file tex 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 $\aut(\mathcal{G})$.
</file>

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==== External links ====
  * [[wp>Graph automorphism]]


{{tag>definition needsreview rjosh rben}}

Abstract Algebra IBL Wiki

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