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Edge-transitive graph

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This is an old revision of this page, as edited by David Eppstein (talk | contribs) at 21:35, 6 May 2008 (the extra elaboration of an "edge-automorphism group" is unnecessary: by Whitney, the symmetries of the line graph are the same as the symmetries of the graph itself). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.
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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