  In this paper, we provide algorithms to rank, unrank, and randomly generate
certain degree-restricted classes of Cayley trees. Specifically, we consider
classes of trees that have a given degree sequence or a given multiset of
degrees. If the underlying set of trees have n vertices, then the largest ranks
involved in each case are of order n! so that it takes O(nlog(n)) bits just to
write down the ranks. Our ranking and unranking algorithms for these
degree-restricted classes are as efficient as can be expected since we show
that they require O(n^2log(n)) bit operations if the underlying trees have n
vertices.
