Nordhaus-Gaddum bounds on the \(k\)-rainbow domatic number of a graph

DOI10.1016/J.AML.2011.04.046zbMath1222.05200OpenAlexW2047205623MaRDI QIDQ550486

Dirk Meierling, Lutz Volkmann, Seyyed Mahmoud Sheikholeslami

Publication date: 11 July 2011

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2011.04.046

zbMATH Keywords

\(k\)-rainbow dominating function\(k\)-rainbow domination number\(k\)-rainbow domatic numberNordhaus-Gaddum bound

Mathematics Subject Classification ID

Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (15)

On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles ⋮ A sharp upper bound on the independent 2-rainbow domination in graphs with minimum degree at least two ⋮ Maximal 2-rainbow domination number of a graph ⋮ The 2-rainbow domination of Sierpiński graphs and extended Sierpiński graphs ⋮ The \(k\)-rainbow bondage number of a graph ⋮ \(k\)-rainbow domatic numbers ⋮ Rainbow reinforcement numbers in digraphs ⋮ The 2-rainbow bondage number in generalized Petersen graphs ⋮ Graphs with large total 2-rainbow domination number ⋮ Unnamed Item ⋮ Rainbow Domination in Graphs ⋮ Total $k$-Rainbow domination numbers in graphs ⋮ Rainbow edge domination numbers in graphs ⋮ Trees with equal total domination and 2-rainbow domination numbers ⋮ The \(k\)-rainbow bondage number of a digraph

Cites Work

• Unnamed Item
• Rainbow domination in graphs
• 2-rainbow domination in generalized petersen graphs \(P(n,3)\)
• Rainbow domination on trees
• 2-rainbow domination of generalized Petersen graphs \(P(n,2)\)
• On the 2-rainbow domination in graphs
• The k-rainbow domatic number of a graph
• Towards a theory of domination in graphs
• On dominating the Cartesian product of a graph and K₂

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