Bounds for Aα-eigenvalues

IF 1.8 4区管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Rairo-Operations Research Pub Date : 2023-09-11 DOI:10.1051/ro/2023144

João Domingos Gomes da Silva Júnior, Carla Silva Oliveira, Liliana Manuela G. C. da Costa

引用次数: 1

Abstract

Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] 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.

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a α-特征值的界

设G为具有邻接矩阵a (G)和度对角矩阵D(G)的图。2017年，Nikiforov[1]将矩阵a α(G)定义为a (G)与D(G)的凸组合，即a α(G) = α a (G) +(1−α)D(G)，其中α∈[0,1]。本文给出了a α-矩阵的最大、第二大和最小特征值的一些新的上界和下界。此外，对达到某些边界的极值图进行了刻画。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Rairo-Operations Research 管理科学-运筹学与管理科学

CiteScore

3.60

自引率

22.20%

发文量

206

审稿时长

>12 weeks

期刊介绍： RAIRO-Operations Research is an international journal devoted to high-level pure and applied research on all aspects of operations research. All papers published in RAIRO-Operations Research are critically refereed according to international standards. Any paper will either be accepted (possibly with minor revisions) either submitted to another evaluation (after a major revision) or rejected. Every effort will be made by the Editorial Board to ensure a first answer concerning a submitted paper within three months, and a final decision in a period of time not exceeding six months.