Strong equality of domination parameters in trees
type: Item
instance of: scholarly article
title: Strong equality of domination parameters in trees
zbMATH Open document ID: 1020.05051
DOI: 10.1016/S0012-365X(02)00451-X
author: Teresa W. Haynes
author: Michael A. Henning
author: Peter Slater
published in: Discrete Mathematics
publication date: 2003-03-16T00:00:00Z
review text: Let \(\gamma(G)\) denote the domination number of graph \(G\), i.e., the minimum cardinality of a dominating vertex set in \(G\), let \(i(G)\) denote the independent domination number of \(G\), i.e., the minimum cardinality of an independent dominating vertex set in \(G\), let \(\gamma_t(G)\) denote the total domination number of graph \(G\), i.e., the minimum cardinality of a totally dominating vertex set in \(G\) (here, the vertices in the dominating set must dominate each other), and let \(\gamma_p(G)\) denote the paired-domination number of graph \(G\), i.e., the minimum cardinality of a dominating vertex set \(S\) in \(G\) such that \(G[S]\) contains at least one perfect matching. This paper gives a constructive characterization of the trees \(T\) for which, first, \(\gamma(T)= i(T)\), second, \(\gamma(T)= \gamma_t(T)\), and third, \(\gamma(T)= \gamma_p(T)\).
reviewed by: Andreas Brandstädt
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 1882180
zbMATH Keywords: domination number
zbMATH Keywords: independent domination
zbMATH Keywords: total domination
zbMATH Keywords: characterization
zbMATH Keywords: trees
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1882180