On equality in an upper bound for the restrained and total domination numbers of a graph

DOI10.1016/j.disc.2007.03.003zbMath1138.05049OpenAlexW2018960846MaRDI QIDQ2461210

Johannes H. Hattingh, Michael A. Henning, David P. Day, Henda C. Swart, Lisa R. Markus, Peter Dankelmann

Publication date: 27 November 2007

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

Full work available at URL: https://doi.org/10.1016/j.disc.2007.03.003

zbMATH Keywords

dominationrestrained dominationtotal domination

Mathematics Subject Classification ID

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

Related Items (15)

Equality in a bound that relates the size and the restrained domination number of a graph ⋮ Bounds on domination parameters in graphs: a brief survey ⋮ Bounds on the total restrained domination number of a graph ⋮ On the ratio between 2-domination and total outer-independent domination numbers of trees ⋮ The product of the restrained domination numbers of a graph and its complement ⋮ On roman, global and restrained domination in graphs ⋮ Total restrained domination in graphs ⋮ On a conjecture involving a bound for the total restrained domination number of a graph ⋮ Total restrained domination in graphs with minimum degree two ⋮ An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree ⋮ Restrained domination in claw-free graphs with minimum degree at least two ⋮ Total restrained domination in claw-free graphs ⋮ Restrained domination in cubic graphs ⋮ Restrained and Total Restrained Domination in Graphs ⋮ A survey of stratified domination in graphs

Cites Work

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• Graphs with large restrained domination number
• Restrained domination in graphs
• Restrained domination in trees
• Trees with equal domination and restrained domination numbers
• On equality in an upper bound for domination parameters of graphs
• Total domination in graphs
• Algorithms for Vertex Partitioning Problems on Partial k-Trees
• Some remarks on domination
• Characterizations of trees with equal domination parameters
• Graphs with large total domination number

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