|Date: Friday, October 28, 2011
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: On the eigenvalues of graphs: results and conjectures
Abstract: In this talk we will discuss two topics. First, upper estimates on the maximal eigenvalue, (Perron-Frobenius eigenvalue), of graphs: undirected, bipartite and directed graphs, with prescribed number of vertices and edges. We will characterize in certain cases the graphs which have the biggest maximal eigenvalue.
Second we will discuss the recent solution of the Grone-Merris conjecture by Hua Bai. This conjecture stated that the eigenvalue sequence of the Laplacian of a given simple undirected graph is majorized by the the dual sequence of the degrees of the graph, and equality holds for threshold graphs.
Speaker: Shmuel Friedland