# 11月30日 郭继明教授学术报告（数学与统计学院）

郭继明, 华东理工大学理学院数学系教授, 博士生导师。主要研究方向为图论与组合数学, 在国内外专业期刊《Linear Algebra and Its Applications》、《DiscreteApplied Mathematics》、《Discrete Mathematics》、《Linear and Multilinear Algebra》、《Journal ofGraph Theory》 、《中国科学》、《Graphs and Combinatorics》等上发表论文60余篇, 被SCI收录50余篇。

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 $A(G)$ isthe adjacency matrix of $G$ and $D(G)=diag(d(v_1),d(v_2),\ldots,d(v_n))$ is thediagonal matrix of vertex degrees of $G$.It is well known that $L(G)$ is apositive semidefinite and symmetric real matrix.Let $S_k(G)$ be the sum of thefirst $k$ largest Laplacian eigenvalues of $G$.It was conjectured by Brouwerthat $S_k(G)\leq e(G)+\binom{k+1}{2}$ holds for $1\leq k\leq n-1$. In thistopic,we propose the improved Brouwer's Laplacian spectrum conjecture and provethe conjecture holds for $k=2$ which

alsoconfirm the conjecture of Guan et al. in 2014.

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