Spectra of strongly Deza graphs
Akbari,Saieed Haemers,Willem H. Hosseinzadeh,Mohammad Ali Kabanov,Vladislav V. Konstantinova,Elena V. Shalaginov,Leonid
Akbari,Saieed
Haemers,Willem H.
Hosseinzadeh,Mohammad Ali
Kabanov,Vladislav V.
Konstantinova,Elena V.
Shalaginov,Leonid
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 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.
Description
Funding Information: This research of the first author was supported by grant number ( G981202 ) from the Sharif University of Technology . The research work of Elena V. Konstantinova is supported by Mathematical Center in Akademgorodok, the agreement with Ministry of Science and Higher Education of the Russian Federation number 075-15-2019-1613 . The research work of M. A. Hosseinzadeh has been supported by a research grant from the Amol University of Special Modern Technologies , Amol, Iran. Publisher Copyright: © 2021 Elsevier B.V.
Date
2021-12
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Keywords
Cospectral graphs, Deza graph, Distance-regular graph, Divisible design graph, Eigenvalues, Strongly regular graph
Citation
Akbari, S, Haemers, W H, Hosseinzadeh, M A, Kabanov, V V, Konstantinova, E V & Shalaginov, L 2021, 'Spectra of strongly Deza graphs', Discrete Mathematics, vol. 344, no. 12, 112622. https://doi.org/10.1016/j.disc.2021.112622