报告学者：潘向峰

报告者单位：安徽大学

报告时间：2025年4月17日（周四）20:00--21:00

报告地点：腾讯会议：868-632-6147

报告摘要：Let $G$ be a simple graph with vertex set $V(G)$ and edge set $E(G)$. The resistance distance between two vertices of $G$ is defined as the effective resistance between these two vertices in the corresponding electrical network where each edge of $G$ is replaced by a unit resistor. The resistance spectrum of a graph is the multiset of resistance distances between all pairs of vertices in the graph. This talk introduces a novel approach for constructing graphs that share the same resistance spectrum. It is established that for any positive integer $k$, there exist at least $2^k$ graphs with identical resistance spectrum. Additionally, it is demonstrated that for $n \geq 10$, there are at least $2((n-10)p(n-9) + q(n-9))$ pairs of graphs of order $n$ with the same resistance spectrum, where $p(n-9)$ represents the number of partitions of the integer $n-9$,and $q(n-9)$ denotes the number of simple graphs of order $n-9$. This is a joint work with Si-Ao Xu and Huan Zhou.

简介：潘向峰，安徽大学数学科学学院教授、博士生导师，院学术、学位委员会成员，安徽省学术和技术带头人后备人选。研究方向为图论与组合网络理论。2006年于中国科学技术大学获得博士学位。曾任中国运筹学会图论组合学分会第四届理事会青年理事以及安徽大学数学科学学院副院长、教授委员会主任。2012年8月，前往美国得克萨斯大学达拉斯分校进行为期一年的访问学习。主持或参与完成国家自然科学项目和国家社科基金项目6项。先后在Discrete Math.、Discrete Appl. Math.、Linear Algebra Appl.、Linear Multilinear Algebra、J. Stat. Phys.、Inf. Process. Lett.、Physica A等学术期刊发表SCI论文60余篇。与他人合作成果两次荣获安徽省科学技术奖三等奖。至今，培养8名博士生获得博士学位。