Classification of vertex-transitive graphs of order a prime cubed - I

Marusic has shown that every vertex-transitive graph of order p(3) is isomorphic to a Cayley graph. Hence to classify vertex-transitive,graphs of order p(3), it suffices to determine necessary and sufficient conditions for two Cayley graphs of a group G of order p(3) to be isomorphic (the isomorphism problem). In this paper, we determine necessary and sufficient conditions for two Cayley graphs of Z(p) x Z(p2) to be isomorphic. In subsequent papers, we will consider the remaining groups of order p(3) for which the isomorphism problem has not been solved. (C) 2000 Elsevier Science B.V. All rights reserved.