On graphs with equal domination and covering numbers
type: Item
instance of: scholarly article
title: On graphs with equal domination and covering numbers
zbMATH Open document ID: 0803.05049
DOI: 10.1016/0166-218X(94)90110-4
author: Lutz Volkmann
published in: Discrete Applied Mathematics
publication date: 1994-07-31T00:00:00Z
review text: A set \(D\) of vertices of a simple graph \(G\) is dominating if every vertex in \(V(G)- D\) is adjacent to some vertex in \(D\), and covering if every edge of \(G\) has at least one end in \(D\). The domination number \(\gamma(G)\) is the minimum order of a dominating set in \(G\). The covering number \(\beta(G)\) is the minimum order of a covering set in \(G\). In this paper, the author characterizes regular graphs, cactus graphs without cycles of length four, chordal graphs, and unicyclic graphs \(G\) for which \(\gamma(G)= \beta(G)\).
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 612446
zbMATH Keywords: covering
zbMATH Keywords: domination number
zbMATH Keywords: dominating set
zbMATH Keywords: covering number
zbMATH Keywords: regular graphs
zbMATH Keywords: cactus graphs
zbMATH Keywords: chordal graphs
zbMATH Keywords: unicyclic graphs
MaRDI profile type: Publication
cites work: Q3208673
cites work: On graphs having domination number half their order
cites work: Q3270978
cites work: Q3933018
cites work: Q3291034
cites work: On domination and independence numbers of graphs
cites work: Q3351385
cites work: Q4008049
cites work: The 1-Factors of Oriented Graphs
cites work: Q3834073
cites work: Q3999465
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description: scientific article; zbMATH DE number 612446