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Edge-transitive graph

In mathematics, an edge-transitive Graph (mathematics) is a graph G such that, given any two edges e1 and e2 of G , there is some Automorphism

: f : G → G

such that

: f ( e1 ) = e2.

In other words, a graph is edge-transitive if its automorphism group (mathematics) acts group action upon its edges.

=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