Eigenvalues and structural properties of graphs
报告题目(Title)：Eigenvalues and structural properties of graphs
报告人(Speaker)：Lai Hongjian （West Virginia University）
地点(Place)：后主楼1129
时间(Time)：2019年12月5日 15:00-16:00
邀请人(Inviter)：徐敏
报告摘要
Let $G$ be a simple graph on $n$ vertices and let $A$ be the adjacency matrix of $G$, and let $\lambda_i(G)$ be the $i$th largest eigenvalue of $A$.Motivated by a problem of Seymour ([Linear Algebra Appl. 437 (2012) 630–647]), Cioaba and Wongproved that for $k \in \{2,3\}$, a condition in terms of an upper bound of $\lambda_2(G)$ to warrant $G$ to have $k$-edge-disjoint spanning trees, and posed a conjecture for all integer $k$ with $k \ge 4$.In [Electronic Journal of Linear Algebra, 34 (2018) 428-443] A. Abiad et al proposed an open problem suggesting to use the $\lambda_2(G)$ to predict the connectivity of $G$. In this talk, we will report the recent progresses and development towards the above-mentioned conjecture and open problems, as well as other related studies.
