文献类型：期刊文献

英文题名：On the full Brouwer's Laplacian spectrum conjecture

作者：Li, Wen-Jun[1];Guo, Ji-Ming[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai, Peoples R China

年份：2022

卷号：345

期号：12

外文期刊名：DISCRETE MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000853708500004)】；

基金：This research is supported by NSFC (No. 12171154) .

语种：英文

外文关键词：Laplacian matrix; Graph; Brouwer?s Laplacian spectrum conjecture

摘要：Let Gbe a simple connected graph and let Sk(G) be the sum of the first klargest Laplacian eigenvalues of G. It was conjectured by Brouwer in 2006 that S-k(G) <= e( G) + (k+1 / 2) holds for 1 <= k <= n - 1. The case k = 2was proved by Haemers, Mohammadian and TayfehRezaie [Linear Algebra Appl., 2010]. In this paper, we propose the full Brouwer's Laplacian spectrum conjecture and we prove the conjecture holds for k = 2which also confirm the conjecture of Guan et al. in 2014.