An upper bound on the total restrained domination number of a tree
type: Item
instance of: scholarly article
title: An upper bound on the total restrained domination number of a tree
zbMATH Open document ID: 1229.90162
author: Johannes H. Hattingh
author: Elizabeth Jonck
author: Ernst J. Joubert
published in: Journal of Combinatorial Optimization
publication date: 2010-11-12T00:00:00Z
review text: Let \(V\) be the set of vertices in a given graph. A subset \(S\) of \(V\) is a total restrained domination set if every vertex is adjacent to a vertex in \(S\) and every vertex not in \(S\) is also adjacent to a vertex in \(V - S\). The total restrained domination number of a graph is the minimum cardinality of a total restrained domination set of the graph. A support vertex is a vertex of degree at least two which is adjacent to a leaf. The authors provide an upper bound on the total restrained domination number of a tree in terms of its order, number of leaves and number of support vertices. Finally, trees are constructively characterized attaining the established bound.
Mathematics Subject Classification ID: 90C27
Mathematics Subject Classification ID: 90C35
zbMATH DE Number: 5815475
zbMATH Keywords: domination number
zbMATH Keywords: total restrained domination tree
MaRDI profile type: Publication
full work available at URL: s10878-008-9204-7
OpenAlex ID: W2000580348
cites work: On total restrained domination in graphs
cites work: Q3412131
cites work: Total restrained domination in trees
cites work: Nordhaus-Gaddum results for restrained domination and total restrained domination in graphs
DOI: 10.1007/S10878-008-9204-7
description: scientific article; zbMATH DE number 5815475