文献类型：期刊文献

英文题名：On the least distance eigenvalue and its applications on the distance spread

作者：Lin, Huiqiu

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2015

卷号：338

期号：6

起止页码：868

外文期刊名：DISCRETE MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000352046000007)】；

基金：The author was supported by the National Natural Science Foundation of China (No. 11401211) and the China Postdoctoral Science Foundation (No. 2014M560303).

语种：英文

外文关键词：Distance spectra; Distance spectral radius; The least distance eigenvalue; Distance spread

摘要：Let G be a connected graph with order n and D(G) be its distance matrix. Suppose that lambda(1) (D) >= ... >= lambda(n)(D) are the distance eigenvalues of G. In this paper, we give an upper bound on the least distance eigenvalue and characterize all the connected graphs with -1 - root 2 <= lambda(n) (D) <= a where a is the smallest root of x(3) - x(2) - 11x - 7 = 0 and a is an element of (-1 - root 2, -2). Furthermore, we show that connected graphs with lambda(n) (D) >= -1 - root 2 are determined by their distance spectra. As applications, we give some lower bounds on the distance spread of graphs with given some parameters. In the end, we characterize connected graphs with the (k + 1)th smallest distance spread. (C) 2015 Elsevier BM. All rights reserved.