文献类型：期刊文献

英文题名：On the Aα-spectra of graphs

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

年份：2018

卷号：556

起止页码：210

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20183005584616);WOS:【SCI-EXPANDED(收录号:WOS:000443667300012)】；

基金：The authors would like to express their gratitude to the anonymous reviewers for their kind suggestions on the original manuscript. The first author was supported by the National Natural Science Foundation of China (No. 11401211) and Fundamental Research Funds for the Central Universities (No. 222201714049). The third author was supported by the National Natural Science Foundation of China (No. 11471121).

语种：英文

外文关键词：A(alpha)-matrix; The k-th largest A(alpha)-eigenvalue; The smallest A(alpha)-eigenvalue

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.