Spectra of Deza graphs

S. Akbari, A. H. Ghodrati, M. A. Hosseinzadeh, V. V. Kabanov, E. V. Konstantinova, L. V. Shalaginov

Research output: Contribution to journalArticle

Abstract

A Deza graph with parameters (n, k, b, a) is a k-regular graph with n vertices such that any two of its vertices have b or a common neighbours, where b ≥ a. 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.

Original languageEnglish
Number of pages12
JournalLinear and Multilinear Algebra
DOIs
Publication statusPublished - 7 Feb 2020

Keywords

  • Deza children
  • Deza graph
  • divisible design graph
  • nullity
  • spectrum of graph
  • PARAMETERS N

Fingerprint Dive into the research topics of 'Spectra of Deza graphs'. Together they form a unique fingerprint.

  • Cite this

    Akbari, S., Ghodrati, A. H., Hosseinzadeh, M. A., Kabanov, V. V., Konstantinova, E. V., & Shalaginov, L. V. (2020). Spectra of Deza graphs. Linear and Multilinear Algebra. https://doi.org/10.1080/03081087.2020.1723472