学术报告

题      目： Spectral conditions for edge-connectivity and edge-disjoint spanning trees in (multi-)graphs

报  告  人：王力工   教授  (邀请人：尤利华 )

                                西北工业大学

时      间：2022-11-08 08:30-10:30

腾 讯 会 议：696 223 024

报告人简介:

       王力工，西北工业大学教授、博士生导师，荷兰Twente大学博士，研究方向为图论及其应用。主持国家自然基金、省、部级基金多项，作为主要成员参加国家自然科学基金多项。在《Journal of Graph Theory》、《Discrete Mathematics》、《Discrete Applied Mathematics》、《Electronic Journal of Combinatorics》、《Linear Algebra and its Applications》等国内外重要学术期刊发表SCI论文110多篇。是国家级精品课程《数学建模》课程和国家级教学成果一等奖的主要参加者。曾获陕西省第九届和第十届自然科学优秀论文一等奖和二等奖各一项。曾被评为陕西省数学建模优秀指导教师和陕西省数学建模优秀组织工作者。曾被评为西北工业大学本科最满意教师。

摘      要：

       A multigraph is a graph with possible multiple edges, but no loops. Let $t$ be a positive integer. Let $\mathcal{G}_{t}$ be the set of simple graphs (or multigraphs) such that for each $G\in\mathcal{G}_{t}$ there exist at least $t+1$ non-empty disjoint proper subsets $V_{1}, V_{2}, \ldots, V_{t+1}\subseteq V(G)$ satisfying $V(G)\setminus(V_{1}\cup V_{2}\cup\cdots\cup V_{t+1})\neq\phi$ and edge connectivity  \kappa'(G)=e(V_{i},V(G)\setminus V_{i})$ for $i=1,2,\ldots,t+1$. Let $D(G)$ and $A(G)$ denote the degree diagonal matrix and adjacency matrix of a simple graph (or a multigraph) $G$, and let $\mu_{i}(G)$ be the $i$th largest eigenvalue of the Laplacian matrix $L(G)=D(G)+A(G)$. In this paper, we investigate the relationship between $\mu_{n-2}(G)$ and edge-connectivity or spanning tree packing number of a graph $G\in\mathcal{G}_{1}$, respectively. We also give the relationship between $\mu_{n-3}(G)$ and edge-connectivity or spanning tree packing number of a graph $G\in\mathcal{G}_{2}$, respectively. Moreover, we generalize all the results about $L(G)$ to a more general matrix $aD(G)+A(G)$, where $a$ is a real number with $a\geq-1$.  This is a joint work with Yang Hu and Cunxiang Duan.