Vertex-transitive graph

In the mathematical field of graph theory, a vertex-transitive graph is a graph G such that, 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 upon its vertices. A graph is vertex-transitive if and only if its graph complement is, since the group actions are identical.