Mutually independent Hamiltonian cycles in k-ary n-cubes when k is even

Authors:
Hsun Su;Jing-Ling Pan;Shin-Shin Kao
Affiliations:
Department of Applied Mathematics, Chung-Yuan Christian University, Chung-Li City 32023, Taiwan, ROC and Department of Public Finance and Taxation, Takming University of Science and Technology, Ta ...;Department of Applied Mathematics, Chung-Yuan Christian University, Chung-Li City 32023, Taiwan, ROC;Department of Applied Mathematics, Chung-Yuan Christian University, Chung-Li City 32023, Taiwan, ROC
Venue:
Computers and Electrical Engineering
Year:
2011

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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 Q"n^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(Q"n^k)|,v(i)@?V(Q"n^k) for 1= be a Hamiltonian cycle of Q"n^k. We prove that Q"n^k contains 2n Hamiltonian cycles, denoted by C"l= for all 0=v"l"^"'(i) for all 2=l^'. The result is optimal since each vertex of Q"n^k has exactly 2n neighbors.