文献类型：期刊文献

英文题名：Graphs determined by their Aα-spectra

作者：Lin, Huiqiu[1];Liu, Xiaogang[2];Xue, Jie[3]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Shanxi, Peoples R China;[3]East China Normal Univ, Dept Comp Sci & Technol, Shanghai 200062, Peoples R China

年份：2019

卷号：342

期号：2

起止页码：441

外文期刊名：DISCRETE MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000453498800016)】；

基金：The authors are grateful to the referees for their careful reading and helpful suggestion. The first author is supported by the National Natural Science Foundation of China (Nos. 11771141 and 11401211) and Fundamental Research Funds for the Central Universities (No. 222201714049). The second author is supported by the National Natural Science Foundation of China (Nos. 11601431 and 61701409); the China Postdoctoral Science Foundation (No. 2016M600813); the Natural Science Foundation of Shaanxi Province (Nos. 2017JQ1019 and 2018JQ6005) and the Fundamental Research Funds for the Central Universities (No. 3102018ZY038).

语种：英文

外文关键词：A(alpha)-spectrum; Determined by the A(alpha)-spectrum; Join

摘要：Let G be a graph with n vertices, and let A(G) and D(G) denote respectively the adjacency matrix and the degree matrix of G. Define A(alpha)(G) = alpha D(G) + (1 - alpha)A(G) for any real alpha is an element of [0, 11]. The collection of eigenvalues of A(alpha)(G) together with multiplicities are called the A(alpha)-spectrum of G. A graph G is said to be determined by its A(alpha)-spectrum if all graphs having the same A(alpha)-spectrum as G are isomorphic to G. We first prove that some graphs are determined by their A(alpha)-spectra for 0 <= alpha < 1, including the complete graph K-n, the union of cycles, the complement of the union of cycles, the union of copies of K2 and K-1, the complement of the union of copies of K-2 and K-1, the path Pei, and the complement of P-n. Setting alpha = 0 or 1/2, those graphs are determined by A- or Q-spectra. Secondly, when G is regular, we show that G is determined by its A(alpha)-spectrum if and only if the join G v Km (m >= 2) is determined by its A(alpha)-spectrum for 1/2 < alpha < 1. Furthermore, we also show that the join K-m boolean OR P-n (m, n >= 2) is determined by its A(alpha)-spectrum for 1/2 < alpha < 1. In the end, we pose some related open problems for future study. (C) 2018 Published by Elsevier B.V.