报告题目：图的距离正则性和特征值
Eigenvalues and distance-regularity of graphs
主讲人：Edwin van Dam教授
报告时间：2017年11月21日下午1:30
报告地点：新光电大楼946
报告摘要：
The eigenvalues of the adjacency matrix of a graph contain a lot --- but not always all --- information on the structure of the graph. In this talk, we will dive deeper into graphs that have a lot of combinatorial symmetry: distance-regular graphs (such as Hamming graphs and Johnson graphs). We will give an overview of when distance-regularity is determined by the eigenvalues (and when it is not). We will see how systems of orthogonal polynomials can help to recognize distance-regular graphs from their eigenvalues and a little extra information through the `spectral excess theorem'.
We then discuss how these methods and ideas led to the construction of the twisted Grassmann graphs, a family of distance-regular graphs that have the same spectrum as certain Grassmann graphs. These twisted graphs are currently the only known family of distance-regular graphs with unbounded diameter that are not vertex-transitive.
报告人介绍：
Edwin van Dam， Full professor of School of Economics and Management, Econometrics and Operations Research Tilburg University. Editor-in-Chief of the Electronic Journal of Combinatorics.