Speaker: Xiaodong ZHANG (Shanghai Jiaotong University)

Time： March 30, 10:00-11:00

Place： 腾讯会议：910-896-042 密码：202203

Title： The Discrete Faber-Krahh Inequality of Graphs

Abstract： The Faber-Krahn inequality states in spectral geometric theory that the ball has smallest first Dirichlet eigenvalue among all bounded domains with the fixed volume in $\mathbb{R}^n$. In this talk, the Dirichlet eigenvalues of graphs with boundary condition were introduced. Then some similar Faber-Krahn inequalities were proved to be held for some classes of graphs, for example the set of all trees and connected unicyclic (bicyclic) graphs with a given graphic unicyclic (bicyclic) degree sequence $\pi$ under minor conditions. Moreover, the extremal unicyclic (bicyclic) graph is unique and possess spiral like ordering and can be regarded as ball approximations. This talk is joined with Guang-Jun Zhang (张光军, 青岛科技大学), Jie Zhang (张杰， 上海立信会计金融学院)