The Hamilton Path in Faulty Enhanced Hypercube

  • Hongmei Liu
  • Yingying Liu
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 126)


So far, the enhanced hypercube \({\mathcal Q}_{\rm n,k}\), where n,k are positive integers with 1≤ k ≤ n–1, is one of the most versatile and efficient interconnection networks (networks for short) for parallel computation. In this paper, the properties related to connectivity in faulty \({\mathcal Q}_{n,k}\) have been investigated through the analysis of the topological structure of n-dimensional enhanced hypercube \({\mathcal Q}_{n,k}\). This study demonstrates that in certain conditions, for any two different vertices there exists a hamilton path connecting x and y. Consequently the enhanced hypercubes are superior in safety.


Bipartite Graph Hamiltonian Path Host Graph Hamiltonian Path Problem Parallel Processing Computer System 
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  1. 1.
    Ascheuer, N.: Hamiltonian path problems in the on-line optimization opf flexible manufacturing systems, PH.D.Thesis, University of Technology, Berlin, Germany (1995)Google Scholar
  2. 2.
    Hsieh, S.Y., Chen, G.H., Ho, C.W.: Fault-free hamiltonian cycles in faulty arrangement graphs. IEEE Trans. Parallel Distri. Syst. 10, 223–237 (1999)CrossRefGoogle Scholar
  3. 3.
    Tsai, C.H., Tan, J.J.M., Liang, T., Hsu, L.H.: Fault-tolerant Hamiltonian laceablity of hypercubes. Information Process Lett. 83, 301–306 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Hsieh, S.Y.: Some edge-fault-tolerant properties of the folded hypercube. Networks, 92–101 (2007)Google Scholar
  5. 5.
    Liu, H.M.: Properties of Enhanced Hypercube Networks. Journal of Systems Science and Information (3), 251–256 (2006)Google Scholar
  6. 6.
    Tsai, C.H.: Linear array and ring embedding in conditional faulty hypercubes. Theorem Computer Science 314, 431–443 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  • Hongmei Liu
    • 1
  • Yingying Liu
    • 1
  1. 1.College of ScienceChina Three Gorges UniversityYichangP.R. China

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