Topological Properties of Hypercubes
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
On k-ary n-cubes: theory and applications
Discrete Applied Mathematics - Special issue: Algorithmic aspects of communication
Graph Theory With Applications
Graph Theory With Applications
Cycles embedding in hypercubes with node failures
Information Processing Letters
Note: Perfect matchings extend to Hamilton cycles in hypercubes
Journal of Combinatorial Theory Series B
Strongly Hamiltonian laceability of the even k-ary n-cube
Computers and Electrical Engineering
The construction of mutually independent Hamiltonian cycles in bubble-sort graphs
International Journal of Computer Mathematics
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The k-ary n-cubes, Qnk, is one of the most well-known interconnection networks in parallel computers. Let n ≥ 1 be an integer and k ≥ 3 be an odd integer. It has been shown that any Qnk is a 2n-regular, vertex symmetric and edge symmetric graph with a hamiltonian cycle. In this article, we prove that any k-ary n-cube contains 2n mutually independent hamiltonian cycles. More specifically, let vi ∈ V(Qnk) for 0 ≤ i ≤ |Qnk| - 1 and let (v0, v1, . . . , v|Qnk|-1, v0) be a hamiltonian cycle of Qnk. We prove that Qnk contains 2n hamiltonian cycles of the form (v0, v1l, . . . , v|Qnk|-1l, v0for 0 ≤ l ≤ 2n - 1, where vil≠ vil′ whenever l ≠ l′. The result is optimal since each vertex of Qnk has exactly 2n neighbors.