  We show that the infinitesimal generator of the symmetric simple exclusion
process, recast as a quantum spin-1/2 ferromagnetic Heisenberg model, can be
solved by elementary techniques on the complete, complete bipartite, and
related multipartite graphs. Some of the resulting infinitesimal generators are
formally identical to homogeneous as well as mixed higher spins models. The
degeneracies of the eigenspectra are described in detail, and the
Clebsch-Gordan machinery needed to deal with arbitrary spin-s representations
of the SU(2) is briefly developed. We mention in passing how our results fit
within the related questions of a ferromagnetic ordering of energy levels and a
conjecture according to which the spectral gaps of the random walk and the
interchange process on finite simple graphs must be equal.
