Edge-transitive graph

In the mathematical field of graph theory, an edge-transitive graph is a graph $G$ such that, given any two edges $e 1$ and $e 2$ of $G$ , there is an automorphism of $G$ that maps $e 1$ to $e 2$ .

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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

Graph families defined by their automorphisms
distance-transitive	→	distance-regular	←	strongly regular
↓
symmetric (arc-transitive)	←	t-transitive, $t \geq 2$		skew-symmetric
↓
_{(if connected)} vertex- and edge-transitive	→	edge-transitive and regular	→	edge-transitive
↓		↓		↓
vertex-transitive	→	regular	→	_{(if bipartite)} biregular
↑
Cayley graph	←	zero-symmetric		asymmetric