Definitions

# 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 an automorphism of G that maps e1 to 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 $K_\left\{m,n\right\}$ is edge-transitive.
• Any edge-transitive graph that is not vertex-transitive is bipartite. These graphs are called semi-symmetric.