On the nonexistence of pseudogeneralized quadrangles
Abstract
In this paper we consider the question of when a strongly regular graph with parameters $((s+1)(st+1),s(t+1),s1,t+1)$ 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 pseudogeneralized quadrangles}. If the graph is a generalized quadrangle then $t \leq s^2$ and $s \leq t^2$, while for pseudogeneralized 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.07609
 Bibcode:
 2019arXiv190907609G
 Keywords:

 Mathematics  Combinatorics