主題：On the improved Brouwer's Laplacian spectrum conjecture
主要內(nèi)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(zhuān)家姓名：郭繼明
工作單位：華東理工大學(xué)
專(zhuān)長(zhǎng)和學(xué)術(shù)成就：圖論，組合數(shù)學(xué)
專(zhuān)家簡(jiǎn)介：郭繼明，華東理工大學(xué)數(shù)學(xué)學(xué)院教授、博士生導(dǎo)師。中國(guó)高等教育學(xué)會(huì)教育數(shù)學(xué)專(zhuān)業(yè)委員會(huì)常務(wù)理事、上海市數(shù)學(xué)會(huì)常務(wù)理事、中國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)理事。主要研究方向?yàn)閳D論與組合數(shù)學(xué)，先后主持多項(xiàng)國(guó)家自然科學(xué)基金面上項(xiàng)目，在國(guó)內(nèi)外雜志上發(fā)表論文80余篇、出版學(xué)術(shù)專(zhuān)著一部。
時(shí)間：2021-11-28 15:30:00
地點(diǎn)：1C323