  We consider the Cayley graph on the symmetric group Sn generated by
derangements. It is well known that the eigenvalues of this grpah are indexed
by partitions of n. We investigate how these eigenvalues are determined by the
shape of their corresponding partitions. In particular, we show that the sign
of an eigenvalue is the parity of the number of cells below the first row of
the corresponding Ferrers diagram. We also provide some lower and upper bounds
for the absolute values of these eigenvalues.
