Eigenvalues and expansion of bipartite graphs

We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of bipartite graphs and give necessary and sufficient conditions for equality. We give several examples of classes that are optimal with respect to the bouns. 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 aclassical bound.