Shamil Asgarli, Sergey Goryainov, Huiqiu Lin, Chi Hoi Yip
Published 2022-01-09, updated 2022-10-18Version 2
We prove that a family of pseudo-Paley graphs of square order obtained from unions of cyclotomic classes satisfies the Erd\H{o}s-Ko-Rado (EKR) module property, in a sense that the characteristic vector of each maximum clique is a linear combination of characteristic vectors of canonical cliques. This extends the EKR-module property of Paley graphs of square order and solves a problem proposed by Godsil and Meagher. Different from previous works, which heavily rely on tools from number theory, our approach is purely combinatorial in nature. The main strategy is to view these graphs as block graphs of orthogonal arrays, which is of independent interest.
Comments: 15 pages; this paper subsumes an earlier preprint by a subset of the authors (arXiv:2104.08839)
All $2$-transitive groups have the EKR-module property
Maximum cliques in pseudo-Paley graphs from unions of cyclotomic classes
On eigenfunctions and maximal cliques of generalised Paley graphs of square order
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