Wilbrink (1984): a $(99,14,1,2)$ graph is not vertex-transitive

No strongly regular graph with parameters $(99,14,1,2)$ is vertex-transitive: if $g$ is such a graph, then it is not the case that for every pair of vertices $v, w$ there is a graph automorphism of $g$ carrying $v$ to $w$.

This is Wilbrink's theorem. In particular a hypothetical $99$-graph cannot be a Cayley graph, which rules out the group-theoretic constructions that produce most known strongly regular graphs — including the two realised members of the family $\lambda = 1$, $\mu = 2$, namely the Paley graph on $9$ vertices and the Berlekamp–van Lint–Seidel graph. The statement is a genuine restriction rather than a vacuous one only in the sense that existence is open; proving it does not require knowing whether such a graph exists.