Edge-transitive graph

[1] In other words, a graph is edge-transitive if its automorphism group acts transitively on its edges.

Subgraphs of complete bipartite graphs Km,n exist when m and n share a factor greater than 2.

When the greatest common factor is 2, subgraphs exist when 2n/m is even or if m=4 and n is an odd multiple of 6.

An edge-transitive graph that is also regular, but still not vertex-transitive, is called semi-symmetric.

The vertex connectivity of an edge-transitive graph always equals its minimum degree.