  We introduce and study a variant of the family of Johnson graphs, the
Full-Flag Johnson graphs. We show that Full-Flag Johnson graphs are Cayley
graphs on S_n generated by certain classes of permutations, and that they are
in fact generalizations of permutahedra. We derive some results about the
adjacency matrices of Full-Flag Johnson graphs and apply these to the set of
permutahedra to deduce part of their spectra.
