Semisymmetric Graphs of Order 2p3 with Valency p2

A simple undirected regular graph is said to be semisymmetric if it is edge-transitive but not vertex-transitive. For a semisymmetric graph Gamma of order 2p(3) , p a prime, it is well known that Gamma is bipartite with two biparts having equal size. The complete classification of such graphs has been given for the full automorphism group Aut( Gamma ) acting unfaithfully on at least one bipart of Gamma , which shows that there is only one infinite family of such graphs with valency p(2) . The graphs of this kind have been determined when Aut( Gamma ) acts faithfully and primitively on at least one bipart of Gamma , and thus there is only one remaining case for classifying such graphs of valency p(2) , Aut( Gamma ) acting faithfully and imprimitively on both biparts of Gamma , which is dealt with in this paper. As a result, there is only one infinite family of semisymmetric graphs of order 2p(3) with valency p(2) .