文献类型：期刊文献

英文题名：More results on the distance (signless) Laplacian eigenvalues of graphs

作者：Xue, Jie[1]; Lin, Huiqiu[2]; Das, Kinkar C.[3]; Shu, Jinlong[1]

机构：[1] Department of Computer Science and Technology, East China Normal University, Shanghai, China; [2] Department of Mathematics, East China University of Science and Technology, Shanghai, China; [3] Department of Mathematics, Sungkyunkwan University, Suwon, Korea, Republic of

年份：2017

外文期刊名：arXiv

收录：EI(收录号：20200526203)

语种：英文

外文关键词：Eigenvalues and eigenfunctions - Laplace transforms - Machine learning

摘要：Let G be a connected graph with vertex set V (G) and edge set E(G). Let T r(G) be the diagonal matrix of vertex transmissions of G and D(G) be the distance matrix of G. The distance Laplacian matrix of G is defined as L(G) = T r(G) - D(G). The distance signless Laplacian matrix of G is defined as Q(G) = T r(G) + D(G). In this paper, we give a lower bound on the distance Laplacian spectral radius in terms of D1, as a consequence, we show that ?L 1 (G) ≥n + ? n ω ?where ! is the clique number of G. Furthermore, we give some graft transformations, by using them, we characterize the extremal graph attains the maximum distance spectral radius in terms of n and !. Moreover, we also give bounds on the distance signless Laplacian eigenvalues of G, and give a confirmation on a conjecture due to Aouchiche and Hansen [4]. Copyright ? 2017, The Authors. All rights reserved.