CAYLEY GRAPHS ISOMORPHIC TO THE PRODUCT OF TWO CAYLEY GRAPHS

Let * be a binary graph operation. We call * a Cayley operation if Gamma(1) * Gamma(2) is a Cayley graph for any two Cayley graphs Gamma(1) and Gamma(2). In this paper, we prove that the cartesian, (categorical or tensor) direct and lexicographic products are Cayley operations. We also investigate the following question: Under what conditions on a binary graph operation * and Cayley graphs Gamma(1) and Gamma(2), the graph product Gamma(1) * Gamma(2) is again a Cayley graph. The latter question is studied for the union, join (sum), replacement and zig-zag products of graphs.