In this paper, we consider the question of when a strongly regular graph with parameters $((s+1)(st+1),s(t+1),s-1,t+1)$ can exist. A strongly regular graph with such parameters is called a pseudo-generalized quadrangle. A pseudo-generalized quadrangle can be derived from a generalized quadrangle, but there are other examples which do not arise in this manner. If the graph is derived from a generalized quadrangle then $t\le s^2$ and $s\le t^2$, while for pseudo-generalized quadrangles we still have the former bound but not the latter. Previously, Neumaier has proved a bound for $s$ which is cubic in $t$, but we improve this to one which is quadratic. The proof involves a careful analysis of cliques and cocliques in the graph. This improved bound eliminates many potential parameter sets which were otherwise feasible.

在本文中，我们考虑以下问题：何时带有参数的强正则图 $（（s+\mathrm{1个}）（sŤ+\mathrm{1个}），s（Ť+\mathrm{1个}），s-\mathrm{1个}，Ť+\mathrm{1个}）$可以存在。具有此类参数的强正则图称为伪广义四边形。伪广义四边形可以从广义四边形派生，但是还有其他一些示例未以这种方式出现。如果图是从广义四边形得出的，则$Ť\le s^2$ 和 $s\le {Ť}^2$，而对于伪广义四边形，我们仍然具有前者约束，而没有后者。以前，诺伊麦尔（Neumaier）已经证明了$s$ 这是立方的 $Ť$，但我们将其改进为二次方。证明包括仔细分析图中的集团和同伴。这种改进的界限消除了许多可能可行的潜在参数集。