Domination and irredundance in the queens' graph
type: Item
instance of: scholarly article
title: Domination and irredundance in the queens' graph
zbMATH Open document ID: 0873.05055
DOI: 10.1016/0012-365X(95)00327-S
author: E. J. Cockayne
author: A. P. Burger
author: Christina M. Mynhardt
published in: Discrete Mathematics
publication date: 1997-10-26T00:00:00Z
review text: The vertices of the queens' graph \(Q_n\) are the squares of an \(n\times n\) chessboard and two squares are adjacent if a queen placed on one covers the other. This paper shows that the domination number of \(Q_n\) is at most \(31n/54+ O(1)\), that \(Q_n\) possesses minimal dominating sets of cardinality \(5n/2- O(1)\) and that the cardinality of any irredundant set of vertices of \(Q_n\) \((n\geq q)\) is at most \(\lfloor 6n+6-8\sqrt{n+\sqrt n+1}\rfloor\).
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 1018616
zbMATH Keywords: queens' graph
zbMATH Keywords: chessboard
zbMATH Keywords: domination number
zbMATH Keywords: dominating sets
zbMATH Keywords: irredundant set
MaRDI profile type: Publication
cites work: Q4309111
cites work: Q4552199
cites work: Q3139865
cites work: Q4871169
cites work: Bibliography on domination in graphs and some basic definitions of domination parameters
cites work: Q4871084
full work available at URL: 0012-365x(95)00327-s
OpenAlex ID: W2071807082
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description: scientific article; zbMATH DE number 1018616