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 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.
Keywords
Cite
@article{arxiv.2201.03100,
title = {The EKR-module property of pseudo-Paley graphs of square order},
author = {Shamil Asgarli and Sergey Goryainov and Huiqiu Lin and Chi Hoi Yip},
journal= {arXiv preprint arXiv:2201.03100},
year = {2023}
}
Comments
15 pages; this paper subsumes an earlier preprint by a subset of the authors (arXiv:2104.08839)