2024/10/05 by Chen, Huye, Goryainov, Sergey, Hu, Cong
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2410.04024
There is a conjecture that the second largest maximal cliques in Paley graphs of square order P(q2) have size (q+ε)/(2), where q ≡ ε\pmod 4, and split into two orbits under the full group of automorphisms whenever q ≥ 25 (a symmetric description for these two orbits is known). However, some extra second largest maximal cliques (of this size) exist in P(q2) whenever q ∈ \9,11,13,17,19,23\. In this paper we analyse the algebraic and geometric structure of the extra cliques.