Speaker: Shmuel Friedland
Date: December 17, 2009
Affiliation: University of Illinois at Chicago

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. <br> Second we will discuss the Grone-Merris conjecture for Laplacians of the eigenvalues of graphs. This conjecture states 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.