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arXiv · 2101.06877

Spectra of strongly Deza graphs

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

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Saieed Akbari, Willem H. Haemers, Mohammad Ali Hosseinzadeh, Vladislav V. Kabanov, Elena V. Konstantinova, Leonid Shalaginov. 2021-01-18. Spectra of strongly Deza graphs. https://doi.org/10.1016/j.disc.2021.112622

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