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] Department of Mathematics, East China University of Science and Technology, Shanhai, 200237, China; [2] Department of Applied Mathematics, Northwestern Polytechnical University Xi’an, Shaanxi, 710072, China; [3] Department of Computer Science and Technology, East China Normal University, Shanghai, 200062, China

年份：2017

外文期刊名：arXiv

收录：EI(收录号：20200035382)

语种：英文

外文关键词：Eigenvalues and eigenfunctions

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 Aα(G) = αD(G) + (1 ? α)A(G) for any real α ∈ [0, 1]. The collection of eigenvalues of Aα(G) together with multiplicities are called the Aα-spectrum of G. A graph G is said to be determined by its Aα-spectrum if all graphs having the same Aα-spectrum as G are isomorphic to G. We first prove that some graphs are determined by its Aα-spectrum for 0 ≤ α 21, those graphs are determined by A- or Q-spectra. Secondly, when G is regular, we show that G is determined by its Aα-spectrum if and only if the join G ∨ Km is determined by its Aα-spectrum for 21 12 Copyright ? 2017, The Authors. All rights reserved.