文献类型：期刊文献

英文题名：Distance signless Laplacian eigenvalues of graphs

作者：Das, Kinkar Chandra[1];Lin, Huiqiu[2];Guo, Jiming[2]

机构：[1]Sungkyunkwan Univ, Dept Math, Suwon 16419, South Korea;[2]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2019

卷号：14

期号：4

起止页码：693

外文期刊名：FRONTIERS OF MATHEMATICS IN CHINA

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000484984300002)】；

基金：The authors are grateful to the two anonymous referees for their careful reading of this paper and strict criticisms, constructive corrections, and valuable comments on this paper, which have considerably improved the presentation of this paper. The first author was supported by the National Research Foundation of the Korean government with grant No. 2017R1D1A1B03028642. The second author was supported by the National Natural Science Foundation of China (Grant No. 11771141) and the Fundamental Research Fund for the Central Universities (No. 222201714049). The third author was supported by the National Natural Science Foundation of China (Grant No. 11371372).

语种：英文

外文关键词：Graph; distance signless Laplacian spectral radius; second largest eigenvalue of distance signless Laplacian matrix; spread

摘要：Suppose that the vertex set of a graph G is V(G) = {v(1), v(2), horizontal ellipsis , v(n)}. The transmission Tr(v(i)) (or D-i) of vertex v(i) is defined to be the sum of distances from v(i) 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 spectral radius of a connected graph G is the spectral radius of the distance signless Laplacian matrix of G, defined as Q(G)=Tr(G)+D(G)\documentclass[12pt], where D(G) is the distance matrix of G. In this paper, we give a lower bound on the distance signless Laplacian spectral radius of graphs and characterize graphs for which these bounds are best possible. We obtain a lower bound on the second largest distance signless Laplacian eigenvalue of graphs. Moreover, we present lower bounds on the spread of distance signless Laplacian matrix of graphs and trees, and characterize extremal graphs.