On the nonexistence of pseudo-generalized quadrangles. (October 2020)

• Record Type: Journal Article
• Authors: Guo, Ivan; Koolen, Jack H.; Markowsky, Greg; Park, Jongyook
• Is Part Of: European journal of combinatorics. Volume 89(2020)
• Publication Date: 2020-10
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2020.103128
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: In this paper, we consider the question of when a strongly regular graph with parameters ( ( s + 1 ) ( s t + 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 ≤ s 2 and s ≤ 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.