Edge-transitive graph

Some graph families defined by their automorphisms
distance-transitive	$\rightarrow$	distance-regular
$\downarrow$
symmetric (arc-transitive)	$\rightarrow$	edge-transitive
$\downarrow$(if connected)
vertex-transitive	$\leftarrow$	Cayley graph
$\downarrow$
regular

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 $K_{m,n}$ is edge-transitive.
• Any edge-transitive graph that is not vertex-transitive is bipartite. These graphs are called semi-symmetric.
• Any symmetric graph is edge-transitive.

See also

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

External links

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