On completely regular graphs with $k=11,$ $\lambda=4$

It is well known that if $\Gamma$ is a connected edge-regular graph with $b_1=1$, then $\Gamma$ is a polygon or a complete multipartite graph $K_{n\times2}$. A. A. Makhnev and his students have studied completely regular graphs with $2\le b_1\le5$. In our earlier article, the study of completely regular graphs with $b_1=6$ was reduced to the investigation of graphs with $k\in\{10,11,12\}$. Together with M. S. Nirova, we considered the case $b_1=6$, $k=10$. This paper deals with completely regular graphs with $b_1=6$ and $k=11$.