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A New Measure for Locally t-Diagnosable Under PMC Model

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Computing and Combinatorics (COCOON 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13025))

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Abstract

PMC model is the test-based diagnosis which a vertex performs the diagnosis by testing the neighbor vertices via the edges between them. Hsu and Tan proposed two structures to diagnose a vertex. But these structures don’t always exist for any vertex. Here, we propose a new testing structure to diagnose a vertex under PMC model to solve the problem above. It can fit more general networks. Let S be a set of faulty edges of the n-dimensional hypercube \(Q_n\). Using this structure, we show that every vertex u of \(Q_n\) is \(\deg _{Q_n-S}(u)\)-diagnosable if \(\delta (Q_n-S)\ge 2\), \(\deg _{Q_n-S}(x)+\deg _{Q_n-S}(y)\ge 5\) for every two adjacent vertices x and y in \(Q_n-S\), and \(n\ge 5\).

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Acknowledgment

This work was supported by Fujian Provincial Department of Science and Technology (2020J01268).

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Authors and Affiliations

  1. School of Applied Mathematics, Xiamen University of Technology, Xiamen, China

    Meirun Chen

  2. Department of Computer and Information Sciences, Fordham University, New York, NY, 10023, USA

    D. Frank Hsu

  3. Department of Computer Science, National Yang Ming Chiao Tung University, Hsinchu, Taiwan

    Cheng-Kuan Lin

Authors
  1. Meirun Chen
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  2. D. Frank Hsu
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  3. Cheng-Kuan Lin
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Corresponding author

Correspondence to Cheng-Kuan Lin .

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Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Chi-Yeh Chen

  2. National Tsing Hua University, Hsinchu, Taiwan

    Wing-Kai Hon

  3. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  4. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

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Chen, M., Hsu, D.F., Lin, CK. (2021). A New Measure for Locally t-Diagnosable Under PMC Model. In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_26

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  • DOI: https://doi.org/10.1007/978-3-030-89543-3_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-89542-6

  • Online ISBN: 978-3-030-89543-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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