TY - JOUR

T1 - Spectra of strongly Deza graphs

AU - Akbari, Saieed

AU - Haemers, Willem H.

AU - Hosseinzadeh, Mohammad Ali

AU - Kabanov, Vladislav V.

AU - Konstantinova, Elena V.

AU - Shalaginov, Leonid

N1 - 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.

PY - 2021/12

Y1 - 2021/12

N2 - 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.

AB - 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.

KW - Cospectral graphs

KW - Deza graph

KW - Distance-regular graph

KW - Divisible design graph

KW - Eigenvalues

KW - Strongly regular graph

U2 - 10.1016/j.disc.2021.112622

DO - 10.1016/j.disc.2021.112622

M3 - Article

AN - SCOPUS:85114780776

SN - 0012-365X

VL - 344

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 12

M1 - 112622

ER -