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In the mathematical field of graph theory, a vertex-transitive graph is a graph G in which, given any two vertices v1 and v2 of G, there is some automorphism
such that
In other words, a graph is vertex-transitive if its automorphism group acts transitively on its vertices. A graph is vertex-transitive if and only if its graph complement is, since the group actions are identical.
Every symmetric graph without isolated vertices is vertex-transitive, and every vertex-transitive graph is regular. However, not all vertex-transitive graphs are symmetric , and not all regular graphs are vertex-transitive.
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