Edge-transitive graph

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This article is about graph theory. For edge transitivity in geometry, see Edge-transitive.

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.

[edit] Examples and properties

• Any complete bipartite graph K_m,n is edge-transitive.
• Any edge-transitive graph that is not vertex-transitive is bipartite. These graphs are called semi-symmetric.

[edit] See also

• Vertex-transitive graph
• Arc-transitive graph
• Edge-transitive (in geometry)

[edit] External links

• Eric W. Weisstein, Edge-transitive graph at MathWorld.