Arc-transitive graph

In mathematics, an arc-transitive graph is a graph G such that, given any two edges e₁ = u₁v₁ and e₂ = u₁v₁ 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.