We provide a substantial improvement on a recent result by Dixit, Kim, and Murty on the
upper bound of $ M_k (n) $, the largest size of a generalized Diophantine tuple with property …

Finding a reasonably good upper bound for the clique number of Paley graphs is an open
problem in additive combinatorics. A recent breakthrough by Hanson and Petridis using …

A well-known conjecture due to van Lint and MacWilliams states that if A is a subset of F q 2
such that 0, 1∈ A,| A|= q, and a− b is a square for each a, b∈ A, then A must be the subfield …

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 …

We describe a new class of maximal cliques, with a vector space structure, of Cayley graphs
defined on the additive group of a field. In particular, we show that in the cubic Paley graph …

We consider generalized Paley graphs Γ (k, q), generalized Paley sum graphs Γ+(k, q), and
their corresponding complements Γ¯(k, q) and Γ¯+(k, q), for k= 3, 4. Denote by Γ= Γ∗(k, q) …

We show that a large multiplicative subgroup of a finite field $\mathbb {F} _q $ cannot be
decomposed into $ A+ A $ or $ A+ B+ C $ nontrivially. We also find new families 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 …