Sun, Liang A result on Vizing’s conjecture. (English) Zbl 1030.05087 Discrete Math. 275, No. 1-3, 363-366 (2004). 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 \(\gamma (G\square H) \geq \gamma(G) \gamma(H)\). Cited in 9 Documents MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) Keywords:Graph; Domination number; Cartesian product PDF BibTeX XML Cite \textit{L. Sun}, Discrete Math. 275, No. 1--3, 363--366 (2004; Zbl 1030.05087) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.