文献类型：期刊文献

英文题名：Characterization of extremal graphs from distance signless Laplacian eigenvalues

作者：Lin, Huiqiu[1];Das, Kinkar Ch.[2]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

年份：2016

卷号：500

起止页码：77

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20161302158348);WOS:【SCI-EXPANDED(收录号:WOS:000374599300007)】；

基金：The authors are much grateful to the anonymous referee for his/her valuable comments on our paper, which have considerably improved the presentation of this paper. The first author is supported by the National Natural Science Foundation of China (Nos. 11401211 and 11471211), the China Postdoctoral Science Foundation (No. 2014M560303) and Fundamental Research Funds for the Central Universities (No. 222201414021). The second author is supported by the National Research Foundation funded by the Korean government with Grant no. 2013R1A1A2009341.

语种：英文

外文关键词：Distance signless Laplacian matrix; Distance signless Laplacian eigenvalues; Independence number

摘要：Let G = (V, E) be a connected graph with vertex set V (G) = {v(1), v(2),..., v(n)} and edge set E(G). The transmission T-r(vi) of vertex vi is defined to be the sum of distances from vi to all other vertices. Let Tr(G) be the n x n diagonal matrix with its (i, i)-entry equal to Tr-G(v(i)). The distance signless Laplacian is defined as D-Q(G) = Tr(G)+ D(G), where D(G) is the distance matrix of G. Let partial derivative(1)(G) > partial derivative(2)(G) >= ... >= partial derivative(n)(G) denote the eigenvalues of distance signless Laplacian matrix of G. In this paper, we first characterize all graphs with partial derivative(n) (G)= n-2. Secondly, we characterize all graphs with partial derivative(2)(G) is an element of [n - 2, n] when n >= 11. Furthermore, we give the lower bound on partial derivative(2)(G) with independence number alpha and the extremal graph is also characterized. (C) 2016 Elsevier Inc. All rights reserved.