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

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 $k-b = 2$.