On the \(\{k\}\)-domination number of Cartesian products of graphs

DOI10.1016/j.disc.2008.07.030zbMath1189.05132OpenAlexW2001588067MaRDI QIDQ1025971

You Lu, Xin Min Hou

Publication date: 23 June 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2008.07.030

zbMATH Keywords

packing numberCartesian productdomination number\(\{k\}\)-domination number

Mathematics Subject Classification ID

Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Graph operations (line graphs, products, etc.) (05C76)

Related Items

From Italian domination in lexicographic product graphs to w-domination in graphs ⋮ Cartesian product graphs and k-tuple total domination ⋮ Domination parameters with number 2: interrelations and algorithmic consequences ⋮ From \(w\)-domination in graphs to domination parameters in lexicographic product graphs ⋮ The Menger number of the Cartesian product of graphs ⋮ Alliance free sets in Cartesian product graphs ⋮ Upper bounds on the balanced \(\langle \mathbf{r}, \mathbf{s} \rangle\)-domination number of a graph ⋮ Some results on Vizing's conjecture and related problems ⋮ The \(\{k\}\)-domatic number of a graph ⋮ 3-tuple total domination number of Rook's graphs ⋮ Vizing's conjecture: a survey and recent results ⋮ Integer domination of Cartesian product graphs ⋮ The integer {k}-domination number of circulant graphs

Cites Work

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• On integer domination in graphs and Vizing-like problems
• On graphs having domination number half their order
• An inequality related to Vizing's conjecture
• A partition approach to Vizing's conjecture
• Vizing's conjecture and the one-half argument