TITLE: Classes of graphs for which isospectrum implies isomorphism?
QUESTION [8 upvotes]: The spectrum of a graph is the (multi)set of eigenvalues of its adjacency matrix (or Laplacian, depending on what you're interested in). In general, two non-isomorphic graphs might have the same spectrum. 
Prompted in part by this discussion on reverse engineering a graph from its spectrum, I was wondering: 

Are there interesting classes of
  graphs for which isospectrality
  implies isomorphism ?

REPLY [4 votes]: If you consider a class of graphs which is closed under taking covering spaces, then this is likely not to work, since one may then apply Sunada's method to construct isospectral pairs.