We study the spectrum of generalized Paley graphs $\Gamma (k, q)= Cay (\mathbb {F} _q,
R_k) $, undirected or not, with $ R_k=\{x^ k: x\in\mathbb {F} _q^*\} $ where $ q= p^ m $ with …

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 consider a special class of generalized Paley graphs over finite fields, namely the
Cayley graphs with vertex set Fqm and connection set the nonzero (qℓ+ 1)-th powers in …

Motivated by the well-known Paley graphs over finite fields and their generalizations, in this
paper we explore a natural multiplicative-additive analogue of such graphs arising from …

We give a reduction formula for the Waring number g (k, q) over a finite field F q. By
exploiting the relation between g (k, q) with the diameter of the generalized Paley graph Γ (k …

We show that the higher Pythagoras numbers for the polynomial ring are infinite $ p_ {2s}(K
[x_1, x_2,\dots, x_n])=\infty $ provided that $ K $ is a real field, $ n\geq2 $ and $ s\geq 1 …

In this paper we study Waring numbers g R (k) for (R, m) a finite commutative local ring with
identity and k∈ N with (k,| R|)= 1. We first relate the Waring number g R (k) with the diameter …

We use known characterizations of generalized Paley graphs which are cartesian
decomposable to explicitly compute the spectra of the corresponding associated irreducible …

In this work we consider the class of Cayley graphs known as generalized Paley graphs (GP-
graphs for short) given by $\Gamma (k, q)= Cay (\mathbb {F} _q,\{x^ k: x\in\mathbb {F} _q^*\}) …

On diagonal equations over finite fields via walks in NEPS of graphs - ScienceDirect Skip to
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