Eigenvalues and the Laplacian of a graph. The Laplacian and
eigenvalues. Basic facts about the spectrum of a graph. Eigenvalues
of weighted graphs. Eigenvalues and random walks. Isoperimetric
problems. History. The Cheeger constant of a graph. The edge
expansion of a graph. The vertex expansion of a graph. A
characterization of the Cheeger constant. Isoperimetric
inequalities for cartesian products. Diameters and eigenvalues. The
diameter of a graph. Eigenvalues and distances between two subsets.
Eigenvalues and distances among many subsets. Eigenvalue upper
bounds for manifolds. Paths, flows, and routing. Paths and sets of
paths. Flows and Cheeger constants. Eigenvalues and routes with
small congestion. Routing in graphs. Comparison theorems.
Eigenvalues and quasi-randomness. Quasi-randomness. The discrepancy
property. The deviation of a graph. Quasi-random graphs.
Bibliography
Chung F.R.K. Lectures on Spectral Graph Theory
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