A regular and edge-transitive graph that is not vertex-transitive is said t
o be semisymmetric. Every semisymmetric graph is necessarily bipartite, wit
h the two parts having equal size and the automorphism group acting transit
ively on each of these two parts. A semisymmetric graph is called biprimiti
ve, ii its automorphism group acts primitively on each part. In this articl
e, a classification of biprimitive semisymmetric graphs arising from the ac
tion of the group PSL(2,p), p = +/-1(mod 8) a prime, acting on cosets of S-
4 is given, resulting in several new infinite families of biprimitive semis
ymmetric graphs. (C) 1999 John Wiley & Sons, Inc.