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Classes of graphs for which isospectrum implies isomorphism ?

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 ?

Suresh Venkat
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