学术报告

题      目： On graphs having minimum Laplacian coefficients

报  告  人：龚世才   教授  (邀请人：尤利华 )

                                浙江科技学院

时      间：2022-11-08 10:30-12:30

腾 讯 会 议：696 223 024

报告人简介:

       博士、教授，浙江科技学院数学学科负责人，研究方向为代数图论、代数组合论及其应用。发表SCI检索论文40多篇，论文引用次数400多次，H指数为12。主持2项国家基金面上项目，4项省级项目。

摘      要：

       Let $G$ be a simple graph with $n$ vertices and $m$ edges and $L(G)$ be its Laplacian matrix. The Laplacian characteristic polynomial of $G$ is defined as $P(G; \la)=\det(\la I-L(G))=\sum_{i=0}^n(-1)^ic_i(G)\la^{n-i}$, where $c_i(G)$ is referred as the $i$-th Laplacian coefficient of $G$. Denote $\mathbf{G}_{n,m}$ by the set of all connected $(n,m)$-graphs. A connected graph $H\in \mathbf{G}_{n,m}$ is called  $c_i$-minimal if $c_i(H)\le c_i(G)$ holds for each $G\in \mathbf{G}_{n,m}$ and is called uniformly minimal if $H$ is $c_i$-minimal for $i=0,1,\ldots,n$.
  In this report, we first prove that each $c_i$-minimal graph in $\mathbf{G}_{n,m}$ is a threshold graph for $2\le i\le n-2$. Then, for a given integer pair $(n,m)$, we investigate the problem of the existence of uniformly minimal graphs in $\mathbf{G}_{n,n+3}$.