Tetravalent ss-transitive graphs of order 4p4p

Let ss be a positive integer. A graph is ss-transitive   if its automorphism group is transitive on ss-arcs but not on (s+1)(s+1)-arcs, and 12-arc-transitive   if its automorphism group is transitive on vertices, edges but not on arcs. Let pp be a prime. Feng et al. [Y.-Q. Feng, K.S. Wang, C.X. Zhou, Tetravalent half-trasnitive graphs of order 4p4p, European J. Combin. 28 (2007) 726–733] classified tetravalent 12-arc-transitive graphs of order 4p4p. In this article a complete classification of tetravalent ss-transitive graphs of order 4p4p is given. It follows from this classification that with the exception of two graphs of orders 88 or 2828, all such graphs are 11-transitive. As a result, all tetravalent vertex- and edge-transitive graphs of order 4p4p are known.