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A result on Vizing’s conjecture. (English) Zbl 1030.05087
Summary: Let $$\gamma(G)$$ denote the domination number of a simple graph $$G$$ and let $$G\square H$$ denote the Cartesian product of two simple graphs $$G$$ and $$H$$. We prove that if $$\gamma(G)=3$$, then $$\gamma (G\square H) \geq \gamma(G) \gamma(H)$$.

##### MSC:
 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
##### Keywords:
Graph; Domination number; Cartesian product
Full Text:
##### References:
 [1] Bondy, J.A.; Murty, U.S.R., Graph theory with applications, (1976), Macmillan Ltd. Press New York · Zbl 1134.05001 [2] Brešar, B., On Vizing’s conjecture, Discuss. math. graph theory, 21, 5-11, (2001) · Zbl 0989.05084 [3] Hartnell, B.; Rall, D.F., Domination in cartesian products: Vizing’s conjecture, (), 163-189 · Zbl 0890.05035 [4] Vizing, V.G., The Cartesian product of graphs, Vyčisl. sistemy, 9, 30-43, (1963) · Zbl 0931.05033
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