Consider a strongly regular graph $G$ with parameters $(76,30,8,14).$ Hoffman's bound tells us that $\overline{G}$ has an independent set of size at most $4$ and its not hard to see there are indeed $4$ independent vertices in $\overline{G}.$

So if $x \in V(G)$ then the graph $H$ induced by $N(v)$ is a $8$-regular, $K_4$-free graph on $30$ vertices and known bounds tell us that $\alpha(H) \ge 5.$

Hence $G$ must must contain $K_{1,5}$ as an induced subgraph. I do not see any way to extend this subgraph without introducing cases.

What I am wondering is

Can someone construct larger graphs that must be present as induced subgraphs of $G$Question 1.

and

Can someone find large induced subgraphs for some of the missing SRG's on less than 100 vertices?Question 2.

The motivating factor for this problem is that getting an induced subgraph of order 19 not having $2$ as an eigenvalue is enough to reconstruct $G.$