Inequality Related to Vizing's Conjecture

14 years 8 days ago

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Let (G) denote the domination number of a graph G and let G H denote the Cartesian product of graphs G and H. We prove that (G)(H) 2(G H) for all simple graphs G and H. 2000 Mathematics Subject Classifications: 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, the Cartesian product G H of G and H is the graph with vertex set V (G)

W. Edwin Clark, Stephen Suen

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