Ricardo A. Podest'a

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math.CO2026

The energy of a family of mirror di-Cayley (sum) graphs: equienergy and moments

Paula M. Chiapparoli, Ricardo A. Podestá

For a group $G$ and subsets $S, T \subset G$ we consider a family of mirror di-Cayley graphs $M X (G; S, T)$ and mirror di-Cayley sums graphs $M X^{+} (G; S, T)$ , namely those with $T=\{e\},…

math.CO2026

On di-Cayley graphs and their spectrum

Paula M. Chiapparoli, Ricardo A. Podesta

Given a group $G$ and three subsets $S_{ℓ}, S_{r}, S_{m} \subset G$ , we consider di-Cayley graphs $D X (G; S_{ℓ}, S_{r}, S_{m})$ and di-Cayley sum graphs $D X^{+} (G; S_{ℓ}, S_{r}, S_{m})$ , directed ge…

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. Podestá, 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. Podestá, Denis E. Videla

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

math.CO2026

Isospectral Cayley graphs with even and odd spectrum

Paula M. Chiapparoli, Ricardo A. Podestá

For a group $G$ and subsets $S, T \subset G$ we introduce the mirror di-Cayley graph $M X (G; S, T)$ and mirror di-Cayley sum graph $M X^{+} (G; S, T)$ with connections sets $S$ and $T$ (MDCG…

The energy of a family of mirror di-Cayley (sum) graphs: equienergy and moments

On di-Cayley graphs and their spectrum

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

Isospectral Cayley graphs with even and odd spectrum

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