Spectra of strongly Deza graphs

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 GA and GB of a Deza graph G are defined on the vertex set of G such that every two distinct vertices are adjacent in GA or GB if and only if t...

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Bibliographic Details
Published in:Discrete mathematics 2021-12, Vol.344 (12), p.112622, Article 112622
Main Authors: Akbari, Saieed, Haemers, Willem H., Hosseinzadeh, Mohammad Ali, Kabanov, Vladislav V., Konstantinova, Elena V., Shalaginov, Leonid
Format: Article
Language:English
Subjects:
Cospectral graphs
Deza graph
Distance-regular graph
Divisible design graph
Eigenvalues
Strongly regular graph
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Summary: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 GA and GB of a Deza graph G are defined on the vertex set of G such that every two distinct vertices are adjacent in GA or GB 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.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2021.112622