TY - UNPB

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

PY - 2021/1

Y1 - 2021/1

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 $G_A$ 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.

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 $G_A$ 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.

M3 - Working paper

T3 - arXiv

BT - Spectra of strongly Deza graphs

PB - Cornell University Library

CY - Ithaca

ER -