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arXiv · 1705.02066

Ovoids of Generalized Quadrangles of Order $(q, q^2-q)$ and Delsarte Cocliques in Related Strongly Regular Graphs

Mohammad Adm·Ryan Bergen·Ferdinand Ihringer·Sam Jaques·Karen Meagher·Alison Purdy·Boting Yang
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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 $(q,q^2-q)$ 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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Mohammad Adm, Ryan Bergen, Ferdinand Ihringer, Sam Jaques, Karen Meagher, Alison Purdy, Boting Yang. 2021-02-11. Ovoids of Generalized Quadrangles of Order $(q, q^2-q)$ and Delsarte Cocliques in Related Strongly Regular Graphs. https://arxiv.org/abs/1705.02066

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