题目：On the Spectral Characterizations of Tournaments

主讲人：西安交通大学  王卫 教授

时间：2021年12月26日(周日) 9:15~10:00

腾讯会议：871 251 058（会议密码：654321）

摘要：

Characterizing graphs by various spectra has long been a central topic in spectral graph theory. However, it is generally very hard to show a given graph to be determined by its spectrum. In this talk, we shall give a simple criterion for a tournament to be determined by its adjacency spectrum. More precisely, let G be a tournament of order n with adjacency matrix A, and W(G)=[e,Ae,…,A^{n-1}e] its walk matrix, where e is the all-one vector. We show that, for any self-converse tournament G, if det W(G) is square-free, then G is uniquely determined by its adjacency spectrum among all tournaments. The result is somewhat unexpected, which was achieved by employing some recent tools for showing a graph to be determined by its generalized spectra. Moreover, some equivalent formulations of the above result, as well as some related ones will also presented. This is a joint work with Wei Wang and LiHong Qiu.

个人简介： 王卫，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/ACM Transactions系列等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。

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