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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.)
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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
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[4] Vizing, V.G., The Cartesian product of graphs, Vyčisl. sistemy, 9, 30-43, (1963) · Zbl 0931.05033
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