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The Pessimistic Diagnosability of Folded Petersen Cubes

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  • Yingli Kang
  • Shuai Ye
  • Weidong Fu
  • Jing Zhu

Abstract

Diagnosability is an important metric parameter for measuring the reliability of multiprocessor systems. The pessimistic diagnosis strategy is a classic diagnostic model based on the PMC model. The class of folded Petersen cubes, denoted by FPQn,k, where n, k ≥ 0 and (n, k) ≠ (0, 0), is introduced as a competitive model of the hypercubes, which is constructed by iteratively applying the Cartesian product operation on the hypercube Qn and the Petersen graph P. In this paper, by exploring the structural properties of the folded Petersen cubes FPQn,k, we first prove that FPQn,k is (n + 3k) diagnosable under the PMC model. Then, we completely derive that the pessimistic diagnosability of FPQn,k is 2n + 6k − 2 under the PMC model. Furthermore, the diagnosability and the pessimistic diagnosability of the class of folded Petersen cubes, including the hypercube, folded Petersen graph, and hyper Petersen graph, are obtained.

Suggested Citation

  • Yingli Kang & Shuai Ye & Weidong Fu & Jing Zhu, 2022. "The Pessimistic Diagnosability of Folded Petersen Cubes," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:3114022
    DOI: 10.1155/2022/3114022
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    References listed on IDEAS

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    1. Taiyin Zhao & Gohar Ali & Nabila Hameed & Syed Inayat Ali Shah & Yu-Ming Chu & Feng Feng, 2020. "The Numerical Invariants concerning the Total Domination for Generalized Petersen Graphs," Journal of Mathematics, Hindawi, vol. 2020, pages 1-5, October.
    2. Zhiqiang Zhang & Muhammad Naeem & Abeera Tariq & Weidong Zhao & Gohar Ali, 2022. "On Square Sum Labeling of Two Families of Petersen Graphs," Journal of Mathematics, Hindawi, vol. 2022, pages 1-14, February.
    3. Zhiqiang Zhang & Muhammad Naeem & Abeera Tariq & Weidong Zhao, 2022. "On Square Sum Labeling of Two Families of Petersen Graphs," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    4. Tingmei Gao & Iftikhar Ahmed & Muhammad Kamran Siddiqui, 2021. "Distance-Based Polynomials and Topological Indices for Hierarchical Hypercube Networks," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, September.
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