| Issue |
RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 2783 - 2798 | |
| DOI | https://doi.org/10.1051/ro/2023144 | |
| Published online | 31 October 2023 | |
Bounds for Aα-eigenvalues
1
Departamento de Engenharia de Produçao - Centro Federal de Educaçao Tecnológica do Rio de Janeiro, Rio de Janeiro, Brazil
2
Departamento de Matemática - Escola Nacional de Ciências Estatísticas, Rio de Janeiro, Brazil
3
Departamento de Matemática - Colégio Pedro II, Rio de Janeiro, Brazil
* Corresponding author: carla.oliveira@ibge.gov.br
Received:
4
April
2023
Accepted:
7
September
2023
Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov (V. Nikiforov, Appl. Anal. Discret. Math. 11 (2017) 81–107.) defined the matrix Aα(G), as a convex combination of A(G) and D(G), the following way, Aα(G) = αA(G) + (1 − α)D(G) where α ∈ [0,1]. In this paper we present some new upper and lower bounds for the largest, second largest and the smallest eigenvalue of Aα-matrix. Moreover, extremal graphs attaining some of these bounds are characterized.
Mathematics Subject Classification: 05C05
Key words: Aα-matrix / Aα-eigenvalues / bounds
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.