In this paper, we consider various topological properties of a k-ary n-cube (Q/sub n//sup k/) using Lee distance. We feel that Lee distance is a natural metric for defining and studying a Q/sub n//sup k/. After defining a Q/sub n//sup k/ graph using Lee distance, we show how to find all disjoint paths between any two nodes. Given a sequence of radix k numbers, a function mapping the sequence to a Gray code sequence is presented, and this function is used to generate a Hamiltonian cycle. Embedding the graph of a mesh and the graph of a binary hypercube into the graph of a Q/sub n//sup k/ is considered. Using a k-ary Gray code, we show the embedding of a k(n/sub 1/)/spl times/k(n/sub 2/)/spl times/.../spl times/k(n/sub m/)-dimensional mesh into a Q/sub n//sup k/ where n=/spl Sigma//sub i=l//sup m/n/sub i/. Then using a single digit, 4-ary reflective Gray code, we demonstrate embedding a Q/sub n/ into Q/sub [n/2]//sup 4/. We look at how Lee distance may be applied to the problem of resource placement in a Q/sub n//sup k/ by using a Lee distance error-correcting code. Although the results in this paper are only preliminary, Lee distance error-correcting codes have not been applied previously to this problem. Finally, we consider how Lee distance can be applied to message routing and single-node broadcasting in a Q/sub n//sup k/. In this section we present two single-node broadcasting algorithms that are optimal when single-port and multi-port I/O is used.>