The EKR-module property of pseudo-Paley graphs of square order

Abstract

We prove that a family of pseudo-Paley graphs of square order obtained from unions of cyclotomic classes satisfies the Erdős-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.

arXiv comment15 pages; this paper subsumes an earlier preprint by a subset of the authors (arXiv:2104.08839)

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Cited by in corpus (4)

• On eigenfunctions and maximal cliques of generalised Paley graphs of square order
• Erdős-Ko-Rado theorem in Peisert-type graphs
• Extremal Peisert-type graphs without the strict-EKR property
• The subspace structure of maximum cliques in pseudo-Paley graphs from unions of cyclotomic classes