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The 1, 2-good-neighbor conditional diagnosabilities of regular graphs

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  • Wei, Yulong
  • Xu, Min

Abstract

Fault diagnosis of systems is an important area of study in the design and maintenance of multiprocessor systems. In 2012, Peng et al. proposed a new measure for the fault diagnosis of systems, namely g-good-neighbor conditional diagnosability, which requires that any fault-free vertex has at least g fault-free neighbors in the system. The g-good-neighbor conditional diagnosabilities of a graph G under the PMC model and the MM* model are denoted by tgPMC(G) and tgMM*(G), respectively. In this paper, we first determine that tgPMC(G)=tgMM*(G) if g ≥ 2. Second, we establish a general result on the 1, 2-good-neighbor conditional diagnosabilities of some regular graphs. As applications, the 1, 2-good-neighbor conditional diagnosabilities of BC graphs, folded hypercubes and four classes of Cayley graphs, namely unicyclic-transposition graphs, wheel-transposition graphs, complete-transposition graphs and tree-transposition graphs, are determined under the PMC model and the MM* model. In addition, we determine the R2-connectivities of BC graphs and folded hypercubes.

Suggested Citation

  • Wei, Yulong & Xu, Min, 2018. "The 1, 2-good-neighbor conditional diagnosabilities of regular graphs," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 295-310.
    • Handle: RePEc:eee:apmaco:v:334:y:2018:i:c:p:295-310
    DOI: 10.1016/j.amc.2018.04.014
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    References listed on IDEAS

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    1. Wang, Shiying & Yang, Yuxing, 2017. "The 2-good-neighbor (2-extra) diagnosability of alternating group graph networks under the PMC model and MM* model," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 241-250.
    2. Tu, Jianhua & Zhou, Yukang & Su, Guifu, 2017. "A kind of conditional connectivity of Cayley graphs generated by wheel graphs," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 177-186.
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