Tetravalent half-arc-transitive graphs of order p5

A graph is half-arc-transitive if its full automorphism group acts transitively on vertices and edges, but not on arcs. Let p be a prime. It is known that there exists no tetravalent half-arc-transitive graph of order p or p2. All the tetravalent half-arc-transitive graphs of order p3 or p4 have been classified in two previous papers [9,23]. As a continuation, in this paper, a classification is given of all tetravalent half-arc-transitive graphs of order p5.