On strongly regular graphs with eigenvalue 2 and their extensions

Let $\mathcal F$ be a class of graphs. A graph $\Gamma$ is called locally $\mathcal F$-graph, if the neighbourhood of each vertex $a$ of $\Gamma$ belongs $\mathcal F$. In the paper it is described the class $\mathcal Q$ of strongly regular graphs with eigenvalue 2 and classified graphs in which the neighbourhood of each vertex is strongly regular with parameters (81,20,1,6).