Denis E. Videla

collaborators

5 papers

math.CO2026

On the number of solutions of systems of diagonal equations through diagonal GP-graphs: the general and the Hermitian-form cases

Ricardo A. Podestá, Denis E. Videla

For any $m, s \in N$ , we study the number $N_{m \times s, q} (κ, β)$ of solutions $(x_{1}, \dots, x_{s}) \in (F_{q})^{s}$ of the monic system of diagonal equations $$ X_{1}^{…

math.CO2026

On $k$ -th unitary Cayley graphs over finite commutative rings: structure and decompositions

Ricardo A. PodestÃ¡, Denis E. Videla

Given $R$ a finite commutative ring with identity and $k \in N$ , we consider the $k$ -th unitary Cayley graph $G_{R} (k) = C a y (R, U_{R, k})$ with $U_{R, k} = {x^{k} : x \in R^{*}}$ ,…

math.CO2026

The nature of the spectrum of generalized Paley graphs and weak Waring numbers over finite fields

Ricardo A. PodestÃ¡, Denis E. Videla

We consider the family of generalized Paley graphs (GP-graphs for short) $I^ (k, q) = C a y (F_{q}, (F_{q}^{*})^{k})$ , with $q = p^{m}$ and $p$ prime. We characterize all GP-graph…

math.CO2025

Connected components and non-bipartiteness of generalized Paley graphs

Ricardo A. PodestÃ¡, Denis E. Videla

In this work we consider the class of Cayley graphs known as generalized Paley graphs (GP-graphs for short) given by $I^ (k, q) = C a y (F_{q}, {x^{k} : x \in F_{q}^{*}})$ ,…

math.CO2025

Spectral properties of generalized Paley graphs

Ricardo A. PodestÃ¡, Denis E. Videla

We study the spectrum of generalized Paley graphs $I^ (k, q) = C a y (F_{q}, R_{k})$ , undirected or not, with $R_{k} = {x^{k} : x \in F_{q}^{*}}$ where $q = p^{m}$ with $p$ prime and $k\mid…

On the number of solutions of systems of diagonal equations through diagonal GP-graphs: the general and the Hermitian-form cases

On k-th unitary Cayley graphs over finite commutative rings: structure and decompositions

The nature of the spectrum of generalized Paley graphs and weak Waring numbers over finite fields

Connected components and non-bipartiteness of generalized Paley graphs

Spectral properties of generalized Paley graphs

On $k$ -th unitary Cayley graphs over finite commutative rings: structure and decompositions