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A family of Hamiltonian and Hamiltonian connected graphs with fault tolerance

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Abstract

Processor (vertex) faults and link (edge) faults may happen when a network is used, and it is meaningful to consider networks (graphs) with faulty processors and/or links. A k-regular Hamiltonian and Hamiltonian connected graph G is optimal fault-tolerant Hamiltonian and Hamiltonian connected if G remains Hamiltonian after removing at most k−2 vertices and/or edges and remains Hamiltonian connected after removing at most k−3 vertices and/or edges. In this paper, we investigate in constructing optimal fault-tolerant Hamiltonian and optimal fault-tolerant Hamiltonian connected graphs. Therefore, some of the generalized hypercubes, twisted-cubes, crossed-cubes, and Möbius cubes are optimal fault-tolerant Hamiltonian and optimal fault-tolerant Hamiltonian connected.

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Authors and Affiliations

  1. Department of Information Management, Ming Hsin University of Science and Technology, Hsin Feng, Hsinchu, 304, Taiwan

    Y-Chuang Chen

  2. Chunghwa Telecom Co., Ltd., 12, Lane 551, Min-Tsu Rd. Sec. 5 Yang-Mei, Taoyuan, 326, Taiwan

    Yong-Zen Huang

  3. Department of Computer Science and Information Engineering, Providence University, Taichung, 433, Taiwan

    Lih-Hsing Hsu

  4. Department of Computer Science, National Chiao Tung University, Hsinchu, 300, Taiwan

    Jimmy J. M. Tan

Authors
  1. Y-Chuang Chen
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  2. Yong-Zen Huang
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  3. Lih-Hsing Hsu
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  4. Jimmy J. M. Tan
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Correspondence to Y-Chuang Chen.

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Chen, YC., Huang, YZ., Hsu, LH. et al. A family of Hamiltonian and Hamiltonian connected graphs with fault tolerance. J Supercomput 54, 229–238 (2010). https://doi.org/10.1007/s11227-009-0316-3

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  • DOI: https://doi.org/10.1007/s11227-009-0316-3

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