题目：On the improved Brouwer's Laplacian spectrum conjecture
摘要：Let G be a simple connected graph with n vertices. The matrix L(G)=D(G)-A(G) is called Laplacian matrix of G, where A(G) is the adjacency matrix of G and D(G)=diag(d(v_1),d(v_2),...,d(v_n)) is the diagonal matrix of vertex degrees of G. It is well known that L(G) is a positive semidefinite and symmetric real matrix. Let S_k(G) be the sum of the first k largest Laplacian eigenvalues of G. It was conjectured by Brouwer that S_k(G)<=e(G)+k(k+1)/2 holds for 1<=k<=n-1. In this topic, we propose the improved Brouwer's Laplacian spectrum conjecture and prove the conjecture holds for k=2 which also confirm the conjecture of Guan et al. in 2014.
时间：2021年11月28日15:30-17:00
地点：文理学院1C323
主讲人: 郭继明
主讲人简介：郭继明，华东理工大学数学学院教授、博士生导师。中国高等教育学会教育数学专业委员会常务理事、上海市数学会常务理事、中国工业与应用数学学会理事。主要研究方向为图论与组合数学，先后主持多项国家自然科学基金面上项目，在国内外杂志上发表论文80余篇、出版学术专著一部。
欢迎广大师生参与！