Abstract Let GP (q 2, m) be the m-Paley graph defined on the finite field with order q 2. We
study eigenfunctions and maximal cliques in generalised Paley graphs GP (q 2, m), where …

Let $ q $ be an odd power of a prime $ p $, and $ S\subset\mathbb {F} _q^* $ such that $ S=-
S $ and $ S/S\neq\mathbb {F} _q^* $. We show that the clique number of the Cayley graph …

Let $ GP (q, d) $ be the $ d $-Paley graph defined on the finite field $\mathbb {F} _q $. It is
notoriously difficult to improve the trivial upper bound $\sqrt {q} $ on the clique number of …

arXiv:2209.00864v2 [math.CO] 6 Sep 2022 Page 1 arXiv:2209.00864v2 [math.CO] 6 Sep 2022
MAXIMALITY OF SUBFIELDS AS CLIQUES IN CAYLEY GRAPHS OVER FINITE FIELDS CHI …

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 …

It is known that Paley graphs of square order have the strict-EKR property, that is, all
maximum cliques are canonical cliques. Peisert-type graphs are natural generalizations of …

The celebrated Erdős–Ko–Rado (EKR) theorem for Paley graphs of square order states that
all maximum cliques are canonical in the sense that each maximum clique arises from the …

We derive an asymptotic formula for the number of solutions in a given subfield to certain
system of equations over finite fields. As an application, we construct new families of …

For a prime p≡ 3 (mod 4) and a positive integer t, let q= p 2 t. The Peisert graph of order q is
the graph with vertex set F q such that ab is an edge if ab∈⟨ g 4⟩∪ g⟨ g 4⟩, where g is a …

We resolve an algebraic version of Schoenberg's celebrated theorem [Duke Math. J., 1942]
characterizing entrywise matrix transforms that preserve positive definiteness. Compared to …