Spectra of strongly Deza graphs

Saieed Akbari, Willem H. Haemers, Mohammad Ali Hosseinzadeh, Vladislav V. Kabanov, Elena V. Konstantinova, Leonid Shalaginov

Research output: Working paperScientific

Abstract

A Deza graph $G$ with parameters $(n,k,b,a)$ is a $k$-regular graph with $n$ vertices such that any two distinct vertices have $b$ or $a$ common neighbours. The children $G_A$ and $G_B$ of a Deza graph $G$ are defined on the vertex set of $G$ such that every two distinct vertices are adjacent in $G_A$ or $G_B$ if and only if they have $a$ or $b$ common neighbours, respectively. A strongly Deza graph is a Deza graph with strongly regular children. In this paper we give a spectral characterisation of strongly Deza graphs, show relationships between eigenvalues, and study strongly Deza graphs which are distance-regular.
Original languageEnglish
Place of PublicationIthaca
PublisherCornell University Library
Number of pages16
Publication statusPublished - Jan 2021

Publication series

NamearXiv
PublisherCornell University
Volume2101.06877

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