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 2022-01, Vol.70 (2), p.310-321
Main Authors: Akbari, S., Ghodrati, A. H., Hosseinzadeh, M. A., Kabanov, V. V., Konstantinova, E. V., Shalaginov, L. V.
Format: Article
Language:English
Subjects:
Apexes
Deza children
Deza graph
divisible design graph
Eigenvalues
Graph theory
Graphs
nullity
spectrum of graph
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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