Inverse problems of graph theory: generalized quadrangles

Graph $\Gamma_i$ for a distance-regular graph $\Gamma$ of diameter 3 can be strongly regular for $i=2$ or $i=3$. Finding parameters of $\Gamma_i$ by the intersection array of graph $\Gamma$ is a direct problem. Finding intersection array of graph $\Gamma$ by the parameters of $\Gamma_i$ is an inverse problem. Earlier direct and inverse problems have been solved by A.A. Makhnev, M.S. Nirova for $i=3$ and by A.A. Makhnev and D.V. Paduchikh for $i=2$.
In this work the inverse problem has been solved in cases when graphs $\Gamma_2$, $\Gamma_3$, $\bar \Gamma_2$ or $\bar \Gamma_3$ are pseudo-geometric for generalized quadrangle. In particular, graphs $\Gamma_2$ and $\bar \Gamma_3$ are not to be a pseudo-geometric for generalized quadrangle.