Graphs with constant sum of domination and inverse domination numbers
type: Item
instance of: scholarly article
title: Graphs with constant sum of domination and inverse domination numbers
zbMATH Open document ID: 1258.05092
DOI: 10.1155/2012/831489
author: T. Tamizh Chelvam
author: T. Asir
published in: International Journal of Combinatorics
publication date: 2012-09-06T00:00:00Z
review text: Summary: A subset \(D\) of the vertex set of a graph \(G\) is a dominating set if every vertex in \(V - D\) is adjacent to at least one vertex in \(D\). The domination number \(\gamma(G)\) is the minimum cardinality of a dominating set of \(G\). A subset of \(V - D\), which is also a dominating set of \(G\) is called an inverse dominating set of \(G\) with respect to \(D\). The inverse domination number \(\gamma'(G)\) is the minimum cardinality of the inverse dominating sets. \textit{G.S. Domke} et al. [Ars Comb. 72, 149--160 (2004; Zbl 1077.05072)] characterized connected graphs \(G\) with \(\gamma(G) + \gamma'(G) = n\), where \(n\) is the number of vertices in \(G\). It is the purpose of this paper to give a complete characterization of graphs \(G\) with minimum degree at least two and \(\gamma(G) + \gamma'(G) = n - 1\).
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 6078075
zbMATH Keywords: dominating set
zbMATH Keywords: domination number
zbMATH Keywords: inverse dominating set
zbMATH Keywords: inverse domination number
Wikidata QID: Q58703372
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/831489
OpenAlex ID: W1971194864
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description: scientific article; zbMATH DE number 6078075