On automorphisms of strongly regular graphs with $\lambda=0$, $\mu=2$

The structure of fixed-point subgraphs of automorphisms of order 3 of strongly regular graphs with parameters $(v,k,0, 2)$ is determined. Let $G$ be the automorphism group of a hypothetical strongly regular graph with parameters $(352, 26, 0, 2)$. Possible orders are found and the structure of fixed-point subgraphs is determined for elements of prime order in $G$. The four-subgroups of $G$ are classified and the possible structure of the group $G$ is determined. A strengthening of a result of Nakagawa on the automorphism groups of strongly regular graphs with $\lambda=0$, $\mu=2$ is obtained.