<p><it>Abstract</it>—In this paper, we consider various topological properties of a <it>k</it>-ary <it>n</it>-cube $<tmath>(Q^k_n)</tmath>$ using Lee distance. We feel that Lee distance is a natural metric for defining and studying a $<tmath>Q^k_n</tmath>$.</p><p>After defining a $<tmath>Q^k_n</tmath>$ graph using Lee distance, we show how to find all disjoint paths between any two nodes. Given a sequence of radix <it>k</it> numbers, a function mapping the sequence to a Gray code sequence is presented, and this function is used to generate a Hamiltonian cycle.</p><p>Embedding the graph of a mesh and the graph of a binary hypercube into the graph of a $<tmath>Q^k_n</tmath>$ is considered. Using a <it>k</it>-ary Gray code, we show the embedding of a $<tmath>k^{n_1}\times k^{n_2}\times \,\,\ldots \,\,\times k^{n_m}-</tmath>$ dimensional mesh into a $<tmath>Q^k_n</tmath>$ where $<tmath>n\,\,=\,\,\sum\nolimits_{i=1}^m {n_i}</tmath>$. Then using a single digit, 4-ary reflective Gray code, we demonstrate embedding a <it>Q</it><sub><it>n</it></sub> into a $<tmath>Q^4_{\lceil {n\over 2}\rceil}</tmath>$.</p><p>We look at how Lee distance may be applied to the problem of resource placement in a $<tmath>Q^k_n</tmath>$ 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.</p><p>Finally, we consider how Lee distance can be applied to message routing and single-node broadcasting in a $<tmath>Q^k_n</tmath>$. In this section we present two single-node broadcasting algorithms that are optimal when single-port and multi-port I/O is used.</p>