Edge-transitive graph

This article is about graph theory. For edge transitivity in geometry, see Edge-transitive.
Graph families defined by their automorphisms
distance-transitive → distance-regular ← strongly regular
↓
symmetric (arc-transitive) ← t-transitive, t ≥ 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

In the mathematical field of graph theory, 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.[1]

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

  1. ^ Biggs, Norman (1993). Algebraic Graph Theory (2nd ed.). Cambridge: Cambridge University Press. p. 118. ISBN 0-521-45897-8.