On the eigenvalues of Aα-matrix of graphs

被引：18

作者：

Liu, Shuting ^{[1
]}

Das, Kinkar Chandra ^{[2
]}

Shu, Jinlong ^{[3
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China

[2] Sungkyunkwan Univ, Dept Math, Suwon 16419, South Korea

[3] East China Normal Univ, Dept Comp Sci & Technol, Shanghai 200062, Peoples R China

来源：

DISCRETE MATHEMATICS | 2020年 / 343卷 / 08期

基金：

新加坡国家研究基金会; 中国国家自然科学基金;

关键词：

Graph; The kth largest eigenvalue of A(alpha)(G); A(alpha)-spectral radius; Degree; SPECTRAL-RADIUS; A(ALPHA)-SPECTRA; CONJECTURES;

D O I：

10.1016/j.disc.2020.111917

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a graph with adjacency matrix A(G) and let D(G) be the diagonal matrix of the degrees of G. For every real alpha is an element of [0, 1], Nikiforov defined the matrix A(alpha)(G) as A(alpha)(G) = alpha D(G)+/- (1 - alpha)A(G). In this paper, we study the kth largest eigenvalue of A(alpha) -matrix of graphs, where 1 <= k <= n. We present several upper and lower bounds on the kth largest eigenvalue of A(alpha-)matrix and characterize the extremal graphs corresponding to some of these obtained bounds. As applications, some bounds we obtained can generalize some known results on adjacency matrix and signless Laplacian matrix of graphs. Finally, we solve a problem proposed by Nikiforov (2017). (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：12

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