Bounds for a alpha-eigenvalues
Discrete Mathematics
2023-01-10 v1
Abstract
Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] defined the matrix Aalpha(G), as a convex combination of A(G) and D(G), the following way, Aalpha(G) = alpha A(G) + (1 - alpha)D(G), where alpha belongs to [0,1]. In this paper, we present some new upper and lower bounds for the largest, second largest, and smallest eigenvalue of the Aalpha-matrix. Moreover, extremal graphs attaining some of these bounds are characterized
Keywords
Cite
@article{arxiv.2301.02733,
title = {Bounds for a alpha-eigenvalues},
author = {João Domingos G. da Silva and Carla Silva Oliveira and Liliana Manuela G. C. da Costa},
journal= {arXiv preprint arXiv:2301.02733},
year = {2023}
}
Comments
14 pages, 3 figures, 2 tables