Some results on domination number of products of graphs

Let G= (V,E) be a simple graph. A subset D of V is called a dominating set of G if for every vertex κ,εV—D,κ is adjacent to at least one vertex of D. Let γ(G) and γ_c (G) denote the domination and connected domination number of G, respectively. In 1965,Vizing conjectured that if GXH is the Cartesian product of G and H, then . In this paper, it is showed that the conjecture holds if Y(H)=#γ _c (H). And for paths P _m and P _n , a lower bound and an upper bound for γ(P _m XP _n ) are obtained. Project supported by National Natural Science Foundation of China.