On the Aα-spectra of graphs

被引：46
作者：
Lin, Huiqiu [1 ]
Xue, Jie [2 ]
Shu, Jinlong [2 ]
机构：
[1] East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China
[2] East China Normal Univ, Dept Comp Sci & Technol, Shanghai, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2018年 / 556卷
基金：
中国国家自然科学基金;
关键词：
A(alpha)-matrix; The k-th largest A(alpha)-eigenvalue; The smallest A(alpha)-eigenvalue; SIGNLESS LAPLACIAN; EIGENVALUE;
D O I：
10.1016/j.laa.2018.07.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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 any real alpha is an element of [0, 1], Nikiforov [8] defined the matrix A(alpha) (G) as A(alpha )(G) = alpha D(G) + (1 - alpha) A(G). In this paper, we give some results on the eigenvalues of A(alpha)(G) for alpha > 1/2. In particular, we characterize the graphs with lambda(k) (A(alpha)(G)) = alpha n - 1 for 2 <= k <= n. Moreover, we show that lambda(n) (A(alpha)(G)) >= 2 alpha - 1 if G contains no isolated vertices. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：210 / 219
页数：10
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