Sulin Song: Eigenvalues of Graphs and Hypergraphs.
Presenter: Sulin Song- Graduate Student Seminar Series
Title: Eigenvalues of Graphs and Hypergraphs.
Abstract: Let $G$ be a graph on $n$ vertices. Its Laplacian matrix is the $n$-by-$n$ matrix $L(G)= D(G)-A(G)$, where $A(G)$ is the familiar (0,1) adjacency matrix, and $D(G)$ is the diagonal matrix of vertex degrees. In this talk, we will introduce results of characterizing graph structure by eigenvalues of the Laplacian matrix or the adjacency matrix, including the classical work of Fiedler in eigenvalues and eigenvectors of Laplacian matrices, as well as the results about the relationship between eigenvalues and the number of edge-disjoint spanning trees. We also talk about the Laplacian matrix on hypergraphs and some of its results.