Tetravalent half-arc-transitive graphs of order p(4)

A graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. It is known that for a prime p there is no tetravalent half-arc-transitive graphs of order p or p(2). Xu [M.Y. Xu, Half-transitive graphs of prime-cube order, J. Algebraic Combin. 1 (1992) 275-282] classified the tetravalent half-arc-transitive graphs of order p(3). As a continuation, we classify in this paper the tetravalent half-arc-transitive graphs of order p(4). It shows that there are exactly p - 1 nonisomorphic connected tetravalent half-arc-transitive graphs of order p4 for each odd prime p. (C) 2007 Elsevier Ltd. All rights reserved.MathematicsSCI(E)0ARTICLE3555-5672