On strongly regular graphs with eigenvalue 2 and their extensions

Undirected strongly regular graphs without loops or multiple edges and with eigenvalues and their extensions are considered. The degree of a vertex is defined as the number of vertices in its neighborhood. For a connected graph in which the neighborhoods of vertices are isomorphic to a strongly regular graph with an eigenvalue of 2, the graph is the union of isolated triangles or is the Gewirtz and its diameter is at most 5. It is also shown that the regular graph is the union of isolated triangles, a quadrangle, or a pentagon, and that it is a pseudogeometric graph. It the strongly regular graph is an amply regular local graph then it is also locally strongly regular graph with parameters (81, 20, 1, 6). The regular graphs are also found to be a distance-regular graph with the intersection array (81, 60, 1; 1, 20, 8).