Edge-transitive graph

In mathematics, an edge-transitive graph is a graph G such that, given any two edges e₁ and e₂ of G, there is some automorphism

f : G → G

such that

f ( e₁ ) = e₂.

In other words, a graph is edge-transitive if its automorphism group acts transitively upon its edges.

Examples and properties

• Any complete bipartite graph K_m,n is edge-transitive.
• Any edge-transitive graph that is not vertex-transitive is bipartite.

See also

• Vertex-transitive graph
• Arc-transitive graph
• Semi-symmetric graph