Mutually independent hamiltonian cycles of binary wrapped butterfly graphs

Authors:
Tz-Liang Kueng;Tyne Liang;Lih-Hsing Hsu
Affiliations:
Department of Computer Science, National Chiao Tung University, 1001 University Road, Hsinchu, 30050, Taiwan, ROC;Department of Computer Science, National Chiao Tung University, 1001 University Road, Hsinchu, 30050, Taiwan, ROC;Department of Computer Science and Information Engineering, Providence University, 200 Chung Chi Road, Taichung, 43301, Taiwan, ROC
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

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Abstract

Effective utilization of communication resources is crucial for improving performance in multiprocessor/communication systems. In this paper, the mutually independent hamiltonicity is addressed for its effective utilization of resources on the binary wrapped butterfly graph. Let G be a graph with N vertices. A hamiltonian cycle C of G is represented by to emphasize the order of vertices on C. Two hamiltonian cycles of G, namely C"1= and C"2=, are said to be independent if u"1=v"1 and u"iv"i for all 2@?i@?N. A collection of m hamiltonian cycles C"1,...,C"m, starting from the same vertex, are m-mutually independent if any two different hamiltonian cycles are independent. The mutually independent hamiltonicity of a graph G, denoted by IHC(G), is defined to be the maximum integer m such that, for each vertex u of G, there exists a set of m-mutually independent hamiltonian cycles starting from u. Let BF(n) denote the n-dimensional binary wrapped butterfly graph. Then we prove that IHC(BF(n))=4 for all n=3.