报告题目：Edge connectivity, edge-disjoint spanning trees and eigenvalues of graphs

报 告 人：王力工教授（西北工业大学）

报告时间：2021年6月19日  9:00-10:00

报告地点：腾讯会议（765310292）

报告摘要：

Let k’(G) and T(G) denote the edge connectivity and the maximum number of edge-disjoint spanning trees of a graph (or a multigraph)G,respectively, where a multigraph is a graph with possible multiple edges but no loops. Let G be the set of simple graphs (or multigraphs) G such that for each G∈G there exists at least two non-empty disjoint proper subsets V1, V2⊆V (G) satisfying V(G)\(V1∪V2) =φand edge connetivity k’(G)=e(Vi, V (G)\Vi) for 1≤i≤2. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of T(G), we mainly present the relations between the third largest(signless Laplacian) eigenvalue and k’(G) or T(G) of a simple graph or a multigraph G∈G, respectively.Inspired by the idea of Cioabă and Gu, we also investigate the relations between the eigenvalues and the existence of spanning k-trees, generalized connectivity and toughness in a graph G with given some parameters, respectively.

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5项，作为主要成员参加国家自然科学基金5项和陕西省自然科学基金1项。现为美国《数学评论》的评论员，在《Discrete Mathematics》《Discrete Applied Mathematics》《Electronic Journal of Combinatorics》《Linear Algebra and its Applications》等国内外学术期刊发表SCI论文100余篇。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。多次指导大学生和研究生参加国际、全国数学建模竞赛，获国际特等奖1项，国际一等奖6项、国际二等奖14项、全国一等奖6项、全国二等奖18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。