Pseudo-geometric graphs of the partial geometries $pG_2(4,t)$

We prove that a strongly regular graph $\Gamma$ with parameters
$$ (10t+5,4t+4,t+3,2t+2), $$
which contains a bad triple coincides with the graph $T(6)$ or with $\bar J(8,4)$. We say that a triple of vertices is bad if these vertices are not pairwise adjacent and the intersection of their neighbourhoods is empty. As a corollary, we establish the fact that any $\lambda$-subgraph of $\Gamma$ consists of isolated vertices and triangles.
This research was supported by the Russian Foundation for Basic Research, grant 99–01–00462.