Edge-transitive graph
From Free net encyclopedia
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.
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Examples and properties
- Any complete bipartite graph <math>K_{m,n}</math> is edge-transitive.
- Any edge-transitive graph that is not vertex-transitive is bipartite.
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