Just to keep the references close to the question, here are two computations of the spectra of a Cayley graph:
Lovász, L. Spectra of graphs with transitive groups. Period. Math. Hungar. 6 (1975), no. 2, 191--195. MR0398886
Babai, L. Spectra of Cayley graphs. J. Combin. Theory Ser. B 27 (1979), no. 2, 180--189. MR0546860
(The prevalence of people named László in this list is interesting. It reminds me of a little story I recently got from Wikipedia while hunting for a reference on the Higman-Sims group: the extraordinary fact that two people named 'Higman' discovered the same sporadic simple group!)
