The class of \(q\)-cliqued graphs: eigen-bi-balanced characteristic, designs, and an entomological experiment
type: Item
instance of: scholarly article
title: The class of \(q\)-cliqued graphs: eigen-bi-balanced characteristic, designs, and an entomological experiment
zbMATH Open document ID: 1322.05097
DOI: 10.1155/2015/152918
author: Paul August Winter
author: Carol Lynne Jessop
author: Costas Zachariades
published in: International Journal of Combinatorics
publication date: 2015-10-06T00:00:00Z
review text: Summary: Much research has involved the consideration of graphs which have subgraphs of a particular kind, such as cliques. Known classes of graphs which are eigen-bi-balanced, that is, they have a pair \(a\), \(b\) of nonzero distinct eigenvalues, whose sum and product are integral, have been investigated. In this paper we will define a new class of graphs, called \(q\)-cliqued graphs, on \(q^2+1\) vertices, which contain \(q\) cliques each of order \(q\) connected to a central vertex, and then prove that these \(q\)-cliqued graphs are eigen-bi-balanced with respect to a conjugate pair whose sum is \(-1\) and product \(1-q\). These graphs can be regarded as design graphs, and we use a specific example in an entomological experiment.
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 6489886
zbMATH Keywords: eigenvalues
zbMATH Keywords: eigen-bi-balanced \(q\)-cliqued graphs
Wikidata QID: Q59106869
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/152918
OpenAlex ID: W2060656337
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description: scientific article; zbMATH DE number 6489886