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- W2059485469 abstract "The k-ary n-cube has been used as the underlying topology for many practical multicomputers, and has been extensively studied in the past. In this article, we will prove that any k-ary n-cube Qn^k, where n>=2 is an integer and k>=4 is an even integer, contains 2n mutually independent Hamiltonian cycles. More specifically, let N=|V(Qn^k)|,v(i)@?V(Qn^k) for 1= be a Hamiltonian cycle of Qn^k. We prove that Qn^k contains 2n Hamiltonian cycles, denoted by Cl= for all 0=vl^'(i) for all 2=l^'. The result is optimal since each vertex of Qn^k has exactly 2n neighbors." @default.
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- W2059485469 date "2011-05-01" @default.
- W2059485469 modified "2023-09-27" @default.
- W2059485469 title "Mutually independent Hamiltonian cycles in k-ary n-cubes when k is even" @default.
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