Edge disjoint Hamiltonian cycles in k-ary n-cubes and hypercubes

Authors:
M. M. Bae;B. Bose
Affiliations:
Unix Clustering Infrastructure, IBM Corp., Poughkeepsie, NY, USA;-
Venue:
IEEE Transactions on Computers
Year:
2003

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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 Zkn 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. Further, 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.