Remarks on the bondage number of planar graphs
type: Item
instance of: scholarly article
title: Remarks on the bondage number of planar graphs
zbMATH Open document ID: 1009.05104
DOI: 10.1016/S0012-365X(02)00449-1
author: Miranca Fischermann
author: Dieter Rautenbach
author: Lutz Volkmann
published in: Discrete Mathematics
publication date: 2003-03-16T00:00:00Z
review text: A subset \(S\) of the vertex set of a graph \(G\) is called dominating in \(G\), if each vertex of \(G\) either is in \(S\), or is adjacent to a vertex of \(S\). The minimum number of vertices of a dominating set in \(G\) is the domination number \(\gamma(G)\) of \(G\). The minimum number of vertices whose deletion from \(G\) changes the value of \(\gamma(G)\) for a higher one, is the bondage number \(b(G)\) of \(G\). This work extends the conjecture that \(b(G) \leq \Delta (G)\) for every connected planar graph to all connected planar graph of girth \(g(G) \geq 4\) and maximum degree at least 5.
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 1882178
zbMATH Keywords: planar graphs
zbMATH Keywords: bondage number
zbMATH Keywords: girth
zbMATH Keywords: domination number
reviewed by: A. Márquez
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1882178