Weighted domination in triangle-free graphs
type: Item
instance of: scholarly article
title: Weighted domination in triangle-free graphs
zbMATH Open document ID: 0995.05111
DOI: 10.1016/S0012-365X(01)00420-4
author: Peter Dankelmann
author: Dieter Rautenbach
author: Lutz Volkmann
published in: Discrete Mathematics
publication date: 2002-08-29T00:00:00Z
review text: The weighted domination number \(\gamma_w(G)\) of a weighted graph \((G,w)\), with positive weights on vertices, is the minimum weight of a dominating set of \(G\). A graph is normed if \(\sum_{v\in V(G)}=|V(G)|\). Earlier, the authors proved the following two Nordhaus-Gaddum type results \[ \gamma_w(G)\cdot\gamma_w(\overline G)\leq\frac{n^2}8 (1+\frac 2{n-2})\quad\text{and}\quad \gamma_w(G)+\gamma_w(\overline G)\leq\frac{3n}4+\frac n{2(n-2)} \] for normed weighted bipartite graphs \((G,w)\) of order \(n\) such that neither \(G\) nor \(\overline G\) has isolated vertices. In this paper, the authors extend these inequalities to normed triangle-free graphs, satisfying the same condition.
reviewed by: Dragan Stevanović
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 1792384
zbMATH Keywords: domination
zbMATH Keywords: weighted graphs
zbMATH Keywords: triangle-free graphs
MaRDI profile type: Publication
full work available at URL: s0012-365x(01)00420-4
OpenAlex ID: W2107328642
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description: scientific article; zbMATH DE number 1792384