Eigenvalues and expansion of bipartite graphs

Abstract

We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of connected bipartite graphs and give necessary and sufficient conditions for equality. We give several examples of classes of graphs that are optimal with respect to the bounds. We prove that BIBD-graphs are characterized by their eigenvalues. Finally we present a new bound on the expansion coefficient of (c, d)-regular bipartite graphs and compare that with with a classical bound.