Abstract
Some new classes of Hamming metric Gray codes over Zpn , where p is a prime and n is an integer power of 2, are described; then, how these Gray codes can be used to generate the maximum number of edge-disjoint Hamiltonian cycles in an n-dimensional generalized hypercube (GHC), Qpn, is shown. For Qpn, the number of edge-disjoint Hamiltonian cycles generated using these methods is n(p -1)/2 which is the maximum possible since the degree of each node in Qpn is n(p - 1). In addition, for any integers p and n, p not necessarily a prime and n not necessarily a power of 2, how to generate the maximum number of edge-disjoint Hamiltonian cycles in Qnp is also described.
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