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][1], I was wondering: 

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


  [1]: https://cstheory.stackexchange.com/questions/3742/reverse-graph-spectra-problem