On strongly regular bicirculants

A necessary condition for the existence of a strongly regular vertex-transitive p-bicirculant, p a prime, is obtained here. In addition, three new strongly regular bicirculants having 50, 82 and 122 vertices corresponding, respectively, to m=3,4 and 5 above, are presented. These graphs are not associated with any Steiner system, and together with their complements form the first known pairs of complementary strongly regular bicirculants which are vertex-transitive but not edge-transitive.