# Deza graphs with parameters (v,k,k-2,a)

## TL;DR

This paper characterizes Deza graphs with parameters where the difference between the degree and the larger common neighbor count is two, expanding understanding beyond the previously studied case where this difference was one.

## Contribution

It provides a complete characterization of Deza graphs with parameters satisfying $k-b=2$, extending prior work on the case $k-b=1$.

## Key findings

- Deza graphs with $k-b=2$ are fully characterized.
- The paper generalizes the classification of Deza graphs.
- New structural properties of these graphs are identified.

## Abstract

A Deza graph with parameters $(v,k,b,a)$ is a $k$-regular graph on $v$ vertices in which the number of common neighbors of two distinct vertices takes two values $a$ or $b$ ($a\leq b$) and both cases exist. In the previous papers Deza graphs with parameters $(v,k,b,a)$ where $k-b = 1$ were characterized. In the paper we characterise Deza graphs with $k-b = 2$.