On hamiltonian circuits in cartesian products of Cayley digraphs

In this paper, we investigate the existence of a hamiltonian circuit in the cartesian product of two Cayley digraphs. Three of our results can be summarized as follows. Suppose K is the Cayley digraph of a dihedral, semidihedral, or dicyclic group arising from a specified pair of (standard) generators, and suppose L is a Cayley digraph with a hamiltonian circuit. Then, the cartesian product of K and L has a hamiltonian circuit. As a corollary to our main theorem, we also show that the cartesian product of an undirected cycle of length n and a directed cycle of length k has a hamiltonian circuit unless n = 2 and k is odd. Some open problems are stated.