arXiv subjects

João Domingos Gomes da Silva Junior

Publications and source records attributed to João Domingos Gomes da Silva Junior.

2 recordsLinked to original sources

arXiv2026

Eigenvalues of $\boldsymbol{L_α}-$matrices under graph operations

Let $G$ be a simple graph, $A(G)$ its adjacency matrix, and $D(G)$ its diagonal degree matrix. In 2022, \citeauthor{Wang2020} (\cite{Wang2020}) defined the family of matrices $L_α$ as the convex linear combination: \[ L_α(G) = αD(G) + (α- 1)A(G), \] where $α\in [0,1]$. The study of the spectrum of this family of matrices may provide a unified framework for analyzing the spectra of the adjacency, degree, and Laplacian matrices ($D(G) - A(G)$). In this work, we investigate the spectrum of $L_α$ under graph operations and within specific families of graphs.

math.CO↗

arXiv2025

Bounds on $A_α$-eigenvalues using graph invariants

In 2017, Nikiforov introduced the concept of the $A_α$-matrix, as a linear convex combination of the adjacency matrix and the degree diagonal matrix of a graph. This matrix has attracted increasing attention in recent years, as it serves as a unifying structure that combines the adjacency matrix and the signless Laplacian matrix. In this paper, we present some bounds for the largest and smallest eigenvalue of $A_α$-matrix involving invariants associated to graphs.

math.CO↗