Spectra of strongly Deza graphs

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

doi:10.1016/j.disc.2021.112622

Spectra of strongly Deza graphs

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

^*Corresponding author for this work

Econometrics and OR

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

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 language	English
Article number	112622
Journal	Discrete Mathematics
Volume	344
Issue number	12
DOIs	https://doi.org/10.1016/j.disc.2021.112622
Publication status	Published - Dec 2021

Keywords

Cospectral graphs
Deza graph
Distance-regular graph
Divisible design graph
Eigenvalues
Strongly regular graph

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10.1016/j.disc.2021.112622

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@article{a5e9a27c1f1f43d1a4b1000e3db2c5cf,

title = "Spectra of strongly Deza graphs",

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.",

keywords = "Cospectral graphs, Deza graph, Distance-regular graph, Divisible design graph, Eigenvalues, Strongly regular graph",

author = "Saieed Akbari and Haemers, {Willem H.} and Hosseinzadeh, {Mohammad Ali} and Kabanov, {Vladislav V.} and Konstantinova, {Elena V.} and Leonid Shalaginov",

note = "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: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = dec,

doi = "10.1016/j.disc.2021.112622",

language = "English",

volume = "344",

journal = "Discrete Mathematics",

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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 -

Spectra of strongly Deza graphs

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Keywords

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