On the domination number of the cartesian product of the cycle of length n and any graph

Let gamma(G) denote the dominatio n number of a graph G and let C mu rectangle G denote the cartesian product of C-n, the cycle of length n >= 3, and G. In this paper, we are mainly concerned with the question: which connected nontrivial graphs satisfy gamma(C-n rectangle G) = gamma(C-n)gamma(G)? We prove that this equality can only hold if n equivalent to 1 (mod 3). In addition, we characterize graphs which satisfy this equality when it = 4 and provide infinite classes of graphs for general n equivalent to 1 (mod 3). (c) 2006 Elsevier B.V. All rights reserved.