Total restrained domination in trees
type: Item
instance of: scholarly article
title: Total restrained domination in trees
zbMATH Open document ID: 1132.05044
author: Johannes H. Hattingh
author: Elizabeth Jonck
author: Ernst J. Joubert
author: Andrew R. Plummer
published in: Discrete Mathematics
publication date: 2007-05-11T00:00:00Z
review text: A subset \(S\) of the vertex set \(V\) of a graph \(G(V, E)\) is a total restrained dominating set if every vertex is adjacent to a vertex in \(S\) and every vertex of \(V-S\) is adjacent to a vertex in \(V-S\). The total restrained domination number of \(G\) is the smallest cardinality of a total restrained dominating set of \(G\). The paper gives lower bounds for the total restrained domination number for trees of order \(n\) and of order \(n = 0\) mod 4. It also constructively characterizes the extremal trees of order \(n\) achieving these lower bounds.
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 5151763
zbMATH Keywords: total restrained domination
zbMATH Keywords: tree
reviewed by: Wai-Kai Chen
MaRDI profile type: Publication
full work available at URL: j.disc.2006.09.014
OpenAlex ID: W2053482026
cites work: Q4350166
cites work: Remarks on restrained domination and total restrained domination in graphs
cites work: Q4368729
cites work: Algorithms for Vertex Partitioning Problems on Partial k-Trees
DOI: 10.1016/J.DISC.2006.09.014
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description: scientific article; zbMATH DE number 5151763