Second eigenvalue and the last eigenvalue
Regarding the last eigenvalue:

The last eigenvalue $\lambda_n$ measures (roughly) how close is the graph to be bipartite. For example, $\lambda_n = -d$ if and only if the graph is bipartite (this is a fairly easy exercise). You can read more about it in Luca Trevisan's blog:

http://lucatrevisan.wordpress.com/2008/06/13/max-cut-and-the-smallest-eigenvalue/

http://lucatrevisan.wordpress.com/2008/09/23/max-cut-gain-and-the-smallest-eigenvalue/