报告题目：Generalized Spectral Characterization of Non-controllable Graphs
报 告 人：王卫 教授
工作单位：西安交通大学
报告时间：2025-11-14 16:00–18:00
报告地点：数信学院305
报告摘要：
A graph $G$ is determined by its generalized spectrum(DGS) if whenever $H$ is a graph such that $H$ and $G$ are cospectral with cospectral complements imply that $H$ is isomorphic to $G$. The existing methods for showing graphs to be DGS work only for controllable or almost controllable graphs, meaning the rank of their walk matrices are equal to $n$ (the order of graphs) $n$ or $n-1$, respectively. It has been an open question as how to show graphs with the rank of walk matrices greater than or equal to $n-2$. In this talk, we fill this gap by giving a new method for showing a family of line graphs to be DGS. This is a joint work with Xinyu Dai, Yizhe Ji and Hao Zhang.
报告人简介：
王卫，西安交通大学数学与统计学院教授、博士生导师。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。在J. Combin. Theory, Ser B, European J. Combin. 以及IEEE/ACM Transactions系列等组合图论刊物上发表研究论文100余篇，主持（完成）国家自然科学基金面上项目多项。目前担任中国运筹学会图论与组合分会常务理事、陕西省工业与应用数学学会理事长及国际刊物“Linear Algebra Appl.”“Discrete Mathematics, Algorithms and Applications”编委等。
