文献类型：期刊文献

英文题名：On the distance and distance Laplacian eigenvalues of graphs

作者：Lin, Huiqiu[1];Wu, Baoyindureng[2];Chen, Yingying[3];Shu, Jinlong[3]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Xinjiang Univ, Coll Math & Syst Sci, Urumqi, Xinjiang, Peoples R China;[3]E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

年份：2016

卷号：492

起止页码：128

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20155001669583);WOS:【SCI-EXPANDED(收录号:WOS:000369562400012)】；

基金：The first author is supported by the National Natural Science Foundation of China (No. 11401211), the China Postdoctoral Science Foundation (No. 2014M560303 and No. 2015T80404) and Fundamental Research Funds for the Central Universities (No. 222201414021). The second author is supported by the National Natural Science Foundation of China (No. 11471211). The third author is supported by the National Natural Science Foundation of China by (No. 11161046) and by Xinjiang Talent Youth Project (No. 2013721012).

语种：英文

外文关键词：Graph; Distance matrix; Distance Laplacian matrix; Distance Laplacian spectral radius

摘要：Let G = (V, E) be a simple graph with vertex set V (G) = {v(1), v(2),...,v(n)} and edge set E(G). Let D(G) be the distance matrix of G. For a given nonnegative integer k, when n is sufficiently large with respect to k, we show that lambda(n-k) (D) <= -1, thereby solving a problem proposed by Lin et al. (2014) [8]. The distance Laplacian spectral radius of a connected graph G is the spectral radius of the distance Laplacian matrix of G, defined as D-L(G) = Tr(G) - D(G), where Tr(G) is the diagonal matrix of vertex transmissions of G. Aouchiche and Hansen (2014) [3] conjectured that m(lambda(1)(D-L)) <= n - 2 when G not congruent to K-n, and the equality holds if and only if either G not congruent to K-1,K-n-1 or G = K-n/2,K-n/2. In this paper, we confirm the conjecture. (C) 2015 Elsevier Inc. All rights reserved.