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arXiv · 2410.04024

Second largest maximal cliques in small Paley graphs of square order

Huye Chen·Sergey Goryainov·Cong Hu
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Abstract

There is a conjecture that the second largest maximal cliques in Paley graphs of square order $P(q^2)$ have size $\frac{q+\epsilon}{2}$, where $q \equiv \epsilon \pmod 4$, and split into two orbits under the full group of automorphisms whenever $q \ge 25$ (a symmetric description for these two orbits is known). However, some extra second largest maximal cliques (of this size) exist in $P(q^2)$ whenever $q \in \{9,11,13,17,19,23\}$. In this paper we analyse the algebraic and geometric structure of the extra cliques.

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Huye Chen, Sergey Goryainov, Cong Hu. 2024-10-05. Second largest maximal cliques in small Paley graphs of square order. https://arxiv.org/abs/2410.04024

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