Group action orbital

Every arc-transitive digraph is an orbital digraph

A (simple) digraph is arc-transitive iff it is the orbital digraph for some permutation group. #m/thm/graph

Proof

Let be an arc-transitive digraph and . Then for any we have . Therefore is an orbital digraph.

Now suppose acts on and let be an orbital. Then iff for some , thus is arc-transitive.

#state/tidy | #lang/en | #SemBr