edge symmetric graph | transitive graph

An edge-transitive graph is a graph such that any two edges are equivalent under some element of its automorphism group. More precisely, a graph is edge-transitive if for all pairs of edges (e_1, e_2) there exists an element γ of the edge automorphism group Aut^*(G) such that γ(e_1) = e_2. Informally speaking, a graph is edge-transitive if every edge has the same local environment, so that no edge can be distinguished from any other based on the vertices and edges surrounding it. By convention, the singleton graph and 2-path graph are considered edge-transitive.

arc-transitive graph | automorphism group | edge automorphism | edge automorphism group | Folkman graph | Gray graph | semisymmetric graph | symmetric graph | vertex-transitive graph