2019/09/17 by Ivan Guo, Jack H. Koolen, Guo, Ivan +5 · 1 citation
Mathematics · Computer Science · #Finite Group Theory Research #Graph theory and applications #Coding theory and cryptography
paper · pdf · doi:10.48550/arxiv.1909.07609
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 ≤ 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.