Maximality of subfields as cliques in Cayley graphs over finite fields

TL;DR

This paper proves that subfields form maximal cliques in certain Cayley graphs over finite fields, confirming a conjecture related to generalized Paley graphs.

Contribution

It establishes the maximality of subfields as cliques in a specific family of Cayley graphs, confirming Yip's conjecture.

Findings

Subfields are maximal cliques in these Cayley graphs.

The result confirms Yip's conjecture on generalized Paley graphs.

The proof applies to a special family of Cayley graphs over finite fields.

Abstract

We show the maximality of subfields as cliques in a special family of Cayley graphs defined on the additive group of a finite field. In particular, this confirms a conjecture of Yip on generalized Paley graphs.