Edge-transitive graph

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 some edge-automorphism

f : E(G) → E(G)

such that

f (e₁) = e₂.

In other words, a graph is edge-transitive if its edge-automorphism group acts transitively upon its edges. An edge-automorphism of a graph is a permutation of the edges that preserves the edge-adjacency relationship. The edge-automorphism group is isomorphic to the vertex-automorphism group of the line graph.

Examples and properties

• Any complete bipartite graph $K_{m,n}$ is edge-transitive.
• Any edge-transitive graph that is not vertex-transitive is bipartite.

See also

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

External links

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