Spectral graph theory (VIII)
by Liz Stanhope
Abstract: We continue our reading of Chapter 1 of Chung's text by improving some of the bounds on the eigenvalues of the normalized Laplacian that were established last week. This will involve extending the definition of the normalized Laplacian to weighted graphs. A discussion of some eigenvalue results for random walks will conclude our treatment of Chapter 1. Next we will begin Chapter 2 by examining the Cheeger constant, and its vertex cut analog, in the setting of the normalized Laplacian.