Matrices and Graphs -- a Two-way Street

Abstract: The interaction between matrices and graphs is fruitful and it benefits both, hence it is a two-way street. In this talk, we will describe some scenery while traveling up and down this street, including sparse matrices, matrix completion, numbers of walks, and connectedness. If time allows, we will stop by a street block and take a closer look at the characterization of Laplacian integral graphs.