Symmetric Squares of Graphs
  We consider symmetric powers of a graph. In particular, we show that the spectra of the symmetric square of strongly regular graphs with the same parameters are equal. We also provide some bounds on the spectra of the symmetric squares of more general graphs. The connection with generic exchange Hamiltonians in quantum mechanics is discussed in an appendix. 
Koenraad Audenaert, Chris Godsil, Gordon Royle and Terry Rudolph