Abstract:
Let $\Gamma$ be a connected edge regular graph with parameters $(v,k,\lambda)$ and $b_1=k-\lambda-1$. Then for every vertices $u,w$ with $d(u,w)=2$ the parameter $\mu(u,w)=k-2b_1+1$, where $1\le x\le2b_1$. In the paper completely regular graphs with $x\le 3$ are classified.