Enumeration of strictly Deza graphs with at most 21 vertices

TL;DR

This paper classifies all strictly Deza graphs with up to 21 vertices, providing a complete enumeration of these specific regular graphs with diameter 2 that are not strongly regular.

Contribution

It presents the first complete enumeration of all strictly Deza graphs with at most 21 vertices, expanding understanding of these graphs' structure.

Findings

Identified 139 strictly Deza graphs up to 21 vertices

Provided a complete classification of these graphs

Enhanced understanding of non-strongly regular Deza graphs

Abstract

A Deza graph $\Gamma$ with parameters $(v,k,b,a)$ is a $k$-regular graph with $v$ vertices such that any two distinct vertices have $b$ or $a$ common neighbours, where $b \ge a$. A Deza graph of diameter 2 which is not a strongly regular graph is called a strictly Deza graph. We find all 139 strictly Deza graphs up to 21 vertices.