Ovoids of Generalized Quadrangles of Order (q, q²-q) and Delsarte Cocliques in Related Strongly Regular Graphs

2017/05/05 by Mohammad Adm, Ryan Bergen, Adm, Mohammad +11
Computer Science · Engineering · Mathematics · #05B05 #05C69 #05E30 #51E12 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1705.02066

openalex publication_date 2017/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate strongly regular graphs for which Hoffman's ratio bound and Cvetcović's inertia bound are equal. This means that ve^- = m^-(e^- - k), where v is the number of vertices, k is the regularity, e^- is the smallest eigenvalue, and m^- is the multiplicity of e^-. We show that Delsarte cocliques do not exist for all Taylor's 2-graphs and for point graphs of generalized quadrangles of order (q,q²-q) for infinitely many q. For cases where equality may hold, we show that for nearly all parameter sets, there are at most two Delsarte cocliques.

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