  In this paper, we show that the eigenvalues of certain classes of Cayley
graphs are integers. The (n,k,r)-arrangement graph A(n,k,r) is a graph with all
the k-permutations of an n-element set as vertices where two k-permutations are
adjacent if they differ in exactly r positions. We establish a relation between
the eigenvalues of the arrangement graphs and the eigenvalues of certain Cayley
graphs. As a result, the conjecture on integrality of eigenvalues of A(n,k,1)
follows.
