On the nonexistence of pseudo-generalized quadrangles

Ivan Guo, Jack H. Koolen, Greg Markowsky, Jongyook Park

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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≤s2 and s≤t2, 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.

Original languageEnglish
Article number103128
Number of pages9
JournalEuropean Journal of Combinatorics
Publication statusPublished - Oct 2020

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