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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.

Examples and properties

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

See also

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