# Department Seminars and Colloquia

### Spectral Graph Theory (IX)

Abstract: We will discuss Chapter 2 of Chung's text, Isoperimetric Problems." Isoperimetric numbers for vertex and edge expansion in the setting of the normalized Laplacian will be defined. We will compare `Cheeger inequalities' for the combinatorial and normalized Laplacian, as well as derive a similar inequality for the vertex expansion setting. Isoperimetric inequalities for Cartesian products of graphs will be given.