文献类型：期刊文献

英文题名：On graphs with at least three distance eigenvalues less than-1

作者：Lin, Huiqiu[1];Zhai, Mingqing[2];Gong, Shicai[3]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Chuzhou Univ, Sch Math Sci, Chuzhou 239012, Anhui, Peoples R China;[3]Zhejiang A&F Univ, Sch Sci, Linan 311300, Zhejiang, Peoples R China

年份：2014

卷号：458

起止页码：548

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20142917942640);WOS:【SCI-EXPANDED(收录号:WOS:000340329300032)】；

基金：Supported by National Natural Science Foundation of China (11101057) and Zhejiang Provincial Natural Science Foundation of China (LY12A01016).

语种：英文

外文关键词：Distance spectra; Distance spectral radius; The second smallest D-eigenvalue

摘要：Let G be a connected graph with order n and D (G) be the distance matrix of G. Suppose that lambda(1)(D) >= lambda(2)(D) >= ... >= lambda(n)(D) are the D-eigenvalue of G. In this paper, we show that lambda(n-1) (D(G)) <= -1 if n >= 4 and lambda(n-2) (D(G)) <= -1 if n >= 7. We also characterize all connected graphs with lambda(n-1) (D(G)) = -1, moreover it is shown that these graphs are determined by their distance spectra. (C) 2014 Elsevier Inc. All rights reserved.