Issue No.10 - October (2003 vol.52)
Myung M. Bae , IEEE Computer Society
Bella Bose , IEEE
<p><b>Abstract</b>—Solutions for decomposing a higher dimensional torus to edge disjoint lower dimensional tori, in particular, edge disjoint Hamiltonian cycles are obtained based on the coding theory approach. First, Lee distance Gray codes in Z_k^n are presented and then it is shown how these codes can directly be used to generate edge disjoint Hamiltonian cycles in <it>k</it>-ary <it>n</it>-cubes. IFurther, some new classes of binary Gray codes are designed from these Lee distance Gray codes and, using these new classes of binary Gray codes, edge disjoint Hamiltonian cycles in hypercubes are generated.</p>
k-ary n-cubes, hypercube, Lee distance, Lee distance Gray codes, binary Gray codes, Hamiltonian cycle.
Myung M. Bae, Bella Bose, "Edge Disjoint Hamiltonian Cycles in k-Ary n-Cubes and Hypercubes", IEEE Transactions on Computers, vol.52, no. 10, pp. 1271-1284, October 2003, doi:10.1109/TC.2003.1234525