On a correspondence between maximal cliques in Paley graphs of square order

TL;DR

This paper establishes a linear fractional correspondence between two types of maximal cliques in Paley graphs of square order, revealing structural insights into their configurations.

Contribution

It introduces a novel linear fractional correspondence linking two classes of maximal cliques in Paley graphs of order q^2, enhancing understanding of their combinatorial structure.

Findings

Identifies a correspondence between two types of maximal cliques

Provides a new perspective on the structure of Paley graphs

Enhances understanding of clique configurations in quadratic order Paley graphs

Abstract

Let $q$ be an odd prime power. Denote by $r(q)$ the value of $q$ modulo 4. In this paper, we establish a linear fractional correspondence between two types of maximal cliques of size $\frac{q+r(q)}{2}$ in the Paley graph of order $q^2$.