Upper bounds on the \(k\)-domination number and the \(k\)-Roman domination number

DOI10.1016/j.dam.2008.10.011zbMath1179.05081OpenAlexW2036644223MaRDI QIDQ1028141

Adriana Hansberg, Lutz Volkmann

Publication date: 30 June 2009

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

Full work available at URL: https://doi.org/10.1016/j.dam.2008.10.011

zbMATH Keywords

domination\(k\)-domination\(k\)-Roman domination

Mathematics Subject Classification ID

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

Related Items (27)

Improved bounds on the \(k\)-tuple (Roman) domination number of a graph ⋮ Computing Roman domatic number of graphs ⋮ On Hop Roman Domination in Trees ⋮ Edge Roman domination on graphs ⋮ Upper bounds on the \(k\)-tuple (Roman) domination number of a graph ⋮ On the strong Roman domination number of graphs ⋮ Data reductions and combinatorial bounds for improved approximation algorithms ⋮ Global Roman domination in graphs ⋮ On the roman domination in the lexicographic product of graphs ⋮ On upper bounds for multiple domination numbers of graphs ⋮ Algorithmic aspects of the \(k\)-domination problem in graphs ⋮ \(k\)-domination and \(k\)-independence in graphs: A survey ⋮ Relating the annihilation number and the 2-domination number of block graphs ⋮ Bounds on the 2-domination number ⋮ Exponential domination in subcubic graphs ⋮ Constructing dominating sets in circulant graphs ⋮ Grundy dominating sequences and zero forcing sets ⋮ On the geodetic and geodetic domination numbers of a graph ⋮ Bounds on the exponential domination number ⋮ A bound on the k-domination number of a graph ⋮ Bounds on weak Roman and 2-rainbow domination numbers ⋮ Varieties of Roman Domination ⋮ Multiple Domination ⋮ Unnamed Item ⋮ Outer-independent total Roman domination in graphs ⋮ Minimum 2-dominating sets in regular graphs ⋮ On general frameworks and threshold functions for multiple domination

Cites Work

• Roman domination in graphs.
• New bounds on the \(k\)-domination number and the \(k\)-tuple domination number
• Dominating a Family of Graphs with Small Connected Subgraphs
• Defendens Imperium Romanum: A Classical Problem in Military Strategy
• An upper bound for thek-domination number of a graph
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