主題：On the improved Brouwer's Laplacian spectrum conjecture
主要內容：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.
專家姓名：郭繼明
工作單位：華東理工大學
專長和學術成就：圖論，組合數學
專家簡介：郭繼明，華東理工大學數學學院教授、博士生導師。中國高等教育學會教育數學專業委員會常務理事、上海市數學會常務理事、中國工業與應用數學學會理事。主要研究方向為圖論與組合數學，先后主持多項國家自然科學基金面上項目，在國內外雜志上發表論文80余篇、出版學術專著一部。
時間：2021-11-28 15:30:00
地點：1C323