Let (G) denote the domination number of a graph G and let GH denote the Cartesian product of graphsG andH. We prove that(G)(H) 2(GH) for all simple graphs G and H. 2000 Mathematics Subject Classications: Primary 05C69, Secondary 05C35 We use V (G), E(G), (G), respectively, to denote the vertex set, edge set and domination number of the (simple) graph G. For a pair of graphs G and H ,t he Cartesian product GH of G and H is the graph with vertex set V (G)V (H )a nd where two vertices are adjacent if and only if they are equal in one coordinate and adjacent in the other. In 1963, V. G. Vizing [2] conjectured that for any graphs G and H,
['W. Edwin Clark', 'Stephen Suen']
Inequality Related to Vizing's Conjecture