An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree

DOI10.1016/j.dam.2009.03.010zbMath1209.05170OpenAlexW1982805968MaRDI QIDQ967326

Johannes H. Hattingh, Ernst J. Joubert

Publication date: 28 April 2010

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

Full work available at URL: https://doi.org/10.1016/j.dam.2009.03.010

zbMATH Keywords

graphupper boundminimum degreedominationrestrained dominationorder of a graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (8)

Bounds on the total restrained domination number of a graph ⋮ NP-completeness and APX-completeness of restrained domination in graphs ⋮ On bondage numbers of graphs: a survey with some comments ⋮ The product of the restrained domination numbers of a graph and its complement ⋮ Unnamed Item ⋮ Restrained domination in claw-free graphs with minimum degree at least two ⋮ Restrained and Total Restrained Domination in Graphs ⋮ A linear time algorithm to compute a minimum restrained dominating set in proper interval graphs

Cites Work

• An upper bound on the total restrained domination number of a tree
• Total restrained domination in trees
• Graphs with large restrained domination number
• Restrained domination in graphs
• Restrained domination in trees
• On equality in an upper bound for the restrained and total domination numbers of a graph
• Nordhaus-Gaddum results for restrained domination and total restrained domination in graphs
• Trees with equal domination and restrained domination numbers
• On equality in an upper bound for domination parameters of graphs
• On total restrained domination in graphs
• Remarks on restrained domination and total restrained domination in graphs
• Algorithms for Vertex Partitioning Problems on Partial k-Trees
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