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.^{[citation needed]}

In other words, a graph is arc-transitive if its automorphism group acts transitively upon its arcs.^{[citation needed]}

Many arc-transitive graphs can be embedded as regular maps.

Examples

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