Arc-transitive graph

Encyclopedia : A : AR : ARC : Arc-transitive graph

In mathematics, an arc-transitive graph is a graph G such that, given any two edges e₁ = u₁v₁ and e₂ = u₂v₂ of G, there are two automorphisms

f : G → G, g : G → G

such that

f (e₁) = e₂, g (e₁) = e₂

and

f (u₁) = u₂, f (v₁) = v₂,

g (u₁) = v₂, g (v₁) = u₂.

In other words, a graph is arc-transitive if its automorphism group acts transitively upon its arcs.

From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.