文献类型：期刊文献

英文题名：On the Aα-spectral radius of a graph

作者：Xue, Jie[1];Lin, Huiqiu[2];Liu, Shuting[1];Shu, Jinlong[1]

机构：[1]East China Normal Univ, Dept Comp Sci & Technol, Shanghai, Peoples R China;[2]East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China

年份：2018

卷号：550

起止页码：105

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20181304954575);WOS:【SCI-EXPANDED(收录号:WOS:000432235400006)】；

基金：The authors would like to thank the anonymous referees very much for valuable suggestions and corrections which lead to a great improvement in the original paper. This work was supported by the National Natural Science Foundation of China (No. 11471121).

语种：英文

外文关键词：Adjacency matrix; Signless Laplacian; Spectral radius; Bounds

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 [3] defined the matrix A(alpha)(G) as A(alpha)(G) = alpha D(G) + (1 - alpha)A(G). The largest eigenvalue of A alpha(G) is called the A(alpha)-spectral radius of G. In this paper, we give three edge graft transformations on A(alpha)-spectral radius. As applications, we determine the unique graph with maximum A(alpha)-spectral radius among all connected graphs with diameter d, and determine the unique graph with minimum A(alpha)-spectral radius among all connected graphs with given clique number. In addition, some bounds on the A(alpha)-spectral radius are obtained. (c) 2018 Elsevier Inc. All rights reserved.