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

AbstractLet γ(G) denote the domination number of a graph G and let Cn□G denote the cartesian product of Cn, the cycle of length n⩾3, and G. In this paper, we are mainly concerned with the question: which connected nontrivial graphs satisfy γ(Cn□G)=γ(Cn)γ(G)? We prove that this equality can only hold if n≡1 (mod3). In addition, we characterize graphs which satisfy this equality when n=4 and provide infinite classes of graphs for general n≡1 (mod3)