An infinite family of biprimitive semisymmetric graphs

A regular and edge-transitive graph that is not vertex-transitive is said to be semisymmetric. Every semisymmetric graph is necessarily bipartite, with the two parts having equal size and the automorphism group acting transitively on each of these two parts. A semisymmetric graph is called biprimitive, if its automorphism group acts primitively on each part. In this article, a classification of biprimitive semisymmetric graphs arising from the action of the group PSL(2, p), p ≡ ±1 (mod 8) a prime, acting on cosets of S₄ is given, resulting in several new infinite families of biprimitive semisymmetric graphs. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 217–228, 1999