Spectra of Deza graphs

A Deza graph with parameters is a k-regular graph with n vertices such that any two of its vertices have b or a common neighbours, where . In this paper we investigate spectra of Deza graphs. In particular, using the eigenvalues of a Deza graph we determine the eigenvalues of its children. Divisible...

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Bibliographic Details
Published in:	Linear & multilinear algebra Vol. 70; no. 2; pp. 310 - 321
Main Authors:	Akbari, S., Ghodrati, A. H., Hosseinzadeh, M. A., Kabanov, V. V., Konstantinova, E. V., Shalaginov, L. V.
Format:	Journal Article
Language:	English
Published:	Abingdon Taylor & Francis 22-01-2022 Taylor & Francis Ltd
Subjects:	Apexes Deza children Deza graph divisible design graph Eigenvalues Graph theory Graphs nullity spectrum of graph
Online Access:	Get full text
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Summary:	A Deza graph with parameters is a k-regular graph with n vertices such that any two of its vertices have b or a common neighbours, where . In this paper we investigate spectra of Deza graphs. In particular, using the eigenvalues of a Deza graph we determine the eigenvalues of its children. Divisible design graphs are significant cases of Deza graphs. Sufficient conditions for Deza graphs to be divisible design graphs are given, a few families of divisible design graphs are presented and their properties are studied. Our special attention goes to the invertibility of the adjacency matrices of Deza graphs.
ISSN:	0308-1087 1563-5139
DOI:	10.1080/03081087.2020.1723472