March 2022 Gauss sums and the maximum cliques in generalized Paley graphs of square order
Chi Hoi Yip
Funct. Approx. Comment. Math. 66(1): 119-138 (March 2022). DOI: 10.7169/facm/1981

Abstract

Let GP(q,d) be the d-Paley graph defined on the finite field Fq. It is notoriously difficult to improve the trivial upper bound q on the clique number of GP(q,d). In this paper, we investigate the connection between Gauss sums over a finite field and the maximum cliques of their corresponding generalized Paley graphs. We show that the trivial upper bound on the clique number of GP(q,d) is tight if and only if d(q+1), which strengthens the previous related results by Broere-Döman-Ridley and Schneider-Silva. We also obtain a new simple proof of Stickelberger's theorem on evaluating semi-primitive Gauss sums.

Citation

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Chi Hoi Yip. "Gauss sums and the maximum cliques in generalized Paley graphs of square order." Funct. Approx. Comment. Math. 66 (1) 119 - 138, March 2022. https://doi.org/10.7169/facm/1981

Information

Published: March 2022
First available in Project Euclid: 22 December 2021

MathSciNet: MR4397683
zbMATH: 1519.05195
Digital Object Identifier: 10.7169/facm/1981

Subjects:
Primary: 11T24
Secondary: 05C69 , 11T30

Keywords: Clique number , Gauss sum , maximum clique , Paley graph

Rights: Copyright © 2022 Adam Mickiewicz University

Vol.66 • No. 1 • March 2022
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