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arXiv · 1909.07609

On the nonexistence of pseudo-generalized quadrangles

Ivan Guo·Jack H. Koolen·Greg Markowsky·Jongyook Park
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Abstract

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. These parameters arise when the graph is derived from a generalized quadrangle, but there are other examples which do not arise in this manner, and we term these {\it pseudo-generalized quadrangles}. If the graph is a generalized quadrangle then $t \leq s^2$ and $s \leq t^2$, 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.

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Ivan Guo, Jack H. Koolen, Greg Markowsky, Jongyook Park. 2019-09-17. On the nonexistence of pseudo-generalized quadrangles. https://arxiv.org/abs/1909.07609

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