题目：Recent Developments on the Generalized Spectral Characterizations of Graphs

主讲人：王卫 教授

时 间：2022年6月6日（周一）上午10：00

地 点：理学院会议室306

主办单位：理学院

主讲人简介：

王卫，男,西安交通大学教授、博士生导师。1991年于浙江大学应用数学专业获理学学士学位，分别于1994年及2002年于西安交通大学获理学硕士及博士学位。主要研究领域为代数图论与组合最优化。在图谱理论的研究中对图的广义谱刻画问题做出了一些原创性的工作，在组合优化领域中对一些NP-困难组合优化问题设计出了一些好的近似算法。目前在J. Combin. Theory, Ser B, European J. Combinatorics,以及IEEE/ACMTransactions系列等国际组合图论顶级刊物上发表研究论文80余篇，主持（完成）国家自然科学基金面上项目三项。

摘要:

“Which graphs are determined by their spectra? ” has been a long-standing unsolved problem in spectral graph theory. The problem originates from chemistry more than 60 years ago and is closely related to many other problems of central interest such as the graph isomorphism problem and the famous problem of Kac “Can one hear the shape of a drum?” It is generally very hard to show a given graph to be determined by its spectrum. We shall consider the problem in the context of the generalized spectrum. We say a graph G is determined by its generalized spectrum, if for any graph H, the graphs H and G are cospectral with cospectral complements imply that H is isomorphic to G. In this talk, I shall report some recent results, as well as some open questions, on this topic.