Bounds on $A_\alpha$-eigenvalues using graph invariants
Combinatorics
2026-05-07 v1
Abstract
In 2017, Nikiforov introduced the concept of the -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 -matrix involving invariants associated to graphs.
Cite
@article{arxiv.2501.03806,
title = {Bounds on $A_\alpha$-eigenvalues using graph invariants},
author = {João Domingos Gomes da Silva Junior and Carla Silva Oliveira and Liliana Manuela Gaspar Cerveira da Costa},
journal= {arXiv preprint arXiv:2501.03806},
year = {2026}
}
Comments
14 pages, 1 figure