Chessboard graphs, related designs, and domination parameters
type: Item
instance of: scholarly article
title: Chessboard graphs, related designs, and domination parameters
zbMATH Open document ID: 0939.05065
DOI: 10.1016/S0378-3758(98)00132-3
author: Charles Wallis
author: Renu C. Laskar
published in: Journal of Statistical Planning and Inference
publication date: 2000-07-05T00:00:00Z
review text: This paper is evidently written for readers who are not specialists in graph theory. It starts with an introduction into graph terminology. Then some classical chessboard problems are described, namely those concerning queens and rooks. Thereafter designs are described and their graphs defined. The chessboard representation of a graph (which is a subgraph of the rook graph) is introduced. Such a representation looks out like a chessboard in which white and black squares occur (not necessarily as on an usual chessboard). The white squares represent the vertices; two vertices are adjacent if and only if the corresponding squares are on the same row or on the same column. The theorems deal with the domination number and the independence number of the line graph of the graph of the \((b,v,r,k,\lambda)\) BIBD and the domination number of the line graph of the classical projective plane \(\text{PG}(2,n)\).
reviewed by: Bohdan Zelinka
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C62
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1326610
zbMATH Keywords: balanced incomplete block design
zbMATH Keywords: chessboard
zbMATH Keywords: queens
zbMATH Keywords: rooks
zbMATH Keywords: domination number
zbMATH Keywords: independence number
zbMATH Keywords: line graph
zbMATH Keywords: projective plane
MaRDI profile type: Publication
Wikidata QID: Q56001811
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full work available at URL: s0378-3758(98)00132-3
OpenAlex ID: W1995808019
description: scientific article; zbMATH DE number 1326610