Graphs having distance-\(n\) domination number half their order
type: Item
instance of: scholarly article
title: Graphs having distance-\(n\) domination number half their order
zbMATH Open document ID: 1004.05044
DOI: 10.1016/S0166-218X(01)00284-0
author: Miranca Fischermann
author: Lutz Volkmann
published in: Discrete Applied Mathematics
publication date: 2002-08-29T00:00:00Z
review text: A set \(D\) of vertices in a graph \(G\) is distance-\(n\) dominating if, for every vertex \(v\in V(G)- D\), there is a vertex \(d\in D\) such that \(\text{dist}(v, d)= n\). The authors give a characterization of graphs \(G\) of diameter at least \(2n-1\) that have a minimum distance-\(n\) dominating set of cardinality \(p/2\), where \(p\) is the order of \(G\). This confirms a conjecture by James W. Boland, Teresa W. Haynes and Linda M. Lawson.
reviewed by: G. Gutin
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 1792316
zbMATH Keywords: dominating sets
zbMATH Keywords: diameter
zbMATH Keywords: distance-\(n\) domination
MaRDI profile type: Publication
cites work: Q4863465
cites work: On graphs having domination number half their order
cites work: Q3313893
cites work: Q4368728
cites work: Q3291034
cites work: Domination-balanced graphs
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description: scientific article; zbMATH DE number 1792316