On the eigenvalues of Aα-matrix of graphs

被引：16

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：

中国国家自然科学基金; 新加坡国家研究基金会;

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

共 50 条

[1] On the eigenvalues and energy of the Aα-matrix of graphs
Konch, Nijara
Bharali, A.
Pirzada, S.
arXiv, 2023,
[2] On the eigenvalues of eccentricity matrix of graphs
Lei, Xingyu
Wang, Jianfeng
Li, Guozheng
DISCRETE APPLIED MATHEMATICS, 2021, 295 : 134 - 147
[3] On Eigenvalues and Energy of Geometric–Arithmetic Matrix of Graphs
S. Pirzada
Bilal A. Rather
M. Aouchiche
Mediterranean Journal of Mathematics, 2022, 19
[4] EIGENVALUES OF ADJACENCY MATRIX OF CUBIC LATTICE GRAPHS
LASKAR, R
PACIFIC JOURNAL OF MATHEMATICS, 1969, 29 (03) : 623 - &
[5] On the eigenvalues of Laplacian ABC-matrix of graphs
Rather, Bilal Ahmad
Ganie, Hilal A.
Li, Xueliang
QUAESTIONES MATHEMATICAE, 2023, 46 (11) : 2403 - 2419
[6] EIGENVALUES OF THE TOPOLOGICAL MATRIX - SPLITTING OF GRAPHS WITH SYMMETRICAL COMPONENTS AND ALTERNANT GRAPHS
MCCLELLAND, BJ
JOURNAL OF THE CHEMICAL SOCIETY-FARADAY TRANSACTIONS II, 1982, 78 : 911 - 916
[7] On eigenvalues of Laplacian matrix for a class of directed signed graphs
Ahmadizadeh, Saeed
Shames, Iman
Martin, Samuel
Nesic, Dragan
LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 523 : 281 - 306
[8] On eigenvalues of the reciprocal distance signless Laplacian matrix of graphs
Alhevaz, Abdollah
Baghipur, Maryam
Alizadeh, Yaser
Pirzada, Shariefuddin
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2021, 14 (10)
[9] On the distribution of eigenvalues of the reciprocal distance Laplacian matrix of graphs
Pirzada, S.
Khan, Saleem
FILOMAT, 2023, 37 (23) : 7973 - 7980
[10] On Eigenvalues and Energy of Geometric-Arithmetic Matrix of Graphs
Pirzada, S.
Rather, Bilal A.
Aouchiche, M.
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (03)

← 1 2 3 4 5 →