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Edge Disjoint Hamiltonian Cycles in k-Ary n-Cubes and Hypercubes
October 2003 (vol. 52 no. 10)
pp. 1271-1284
Myung M. Bae, IEEE Computer Society
Bella Bose, IEEE

Abstract—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 k-ary n-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.

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Index Terms:
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, Oct. 2003, doi:10.1109/TC.2003.1234525
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