Vertex-Transitive Digraphs of Order $p^5$ are Hamiltonian

Abstract

We prove that connected vertex-transitive digraphs of order $p^{5}$ (where $p$ is a prime) are Hamiltonian, and a connected digraph whose automorphism group contains a finite vertex-transitive subgroup $G$ of prime power order such that $G'$ is generated by two elements or elementary abelian is Hamiltonian.