文献类型：期刊文献

英文题名：A note on the Aα-spectral radius of graphs

作者：Lin, Huiqiu[1];Huang, Xing[1];Xue, Jie[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：557

起止页码：430

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20183305700570);WOS:【SCI-EXPANDED(收录号:WOS:000444926700022)】；

基金：Supported by National Natural Science Foundation of China (Nos. 11401211 and 11471121) and Fundamental Research Funds for the Central Universities (No. 222201714049).

语种：英文

外文关键词：A(alpha)-matrix; A(alpha)-spectral radius; Cut vertex; Matching number

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 (2017) [7] defined the matrix A(alpha) (G) as A(alpha)(G) = alpha D(G) + (1 - alpha)A(G). Let u and v be two vertices of a connected graph G. Suppose that u and v are connected by a path w(0) (= v)w(1) . . . w(s-1)ws (= u) where d(w(i)) = 2 for 1 <= i <= s - 1. Let G(p, s, q) (u, v) be the graph obtained by attaching the paths P-p to u and P-q to v. Let s = 0, 1. Nikiforov and Rojo (2018) [9] conjectured that rho(alpha) (G(p, s, q) (u , v)) < rho(alpha) (G(p, s, q) (u , v)) if p > q + 2. In this paper, we confirm the conjecture. As applications, firstly, the extremal graph with maximal A(alpha)-spectral radius with fixed order and cut vertices is characterized. Secondly, we characterize the extremal tree which attains the maximal A(alpha)-spectral radius with fixed order and matching number. These results generalize some known results. (C) 2018 Elsevier Inc. All rights reserved.