 The 1, 2-good-neighbor conditional diagnosabilities of regular graphsYulong Wei and Min Xu Applied Mathematics and Computation, 2018, vol. 334, issue C, 295-310 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. Keywords: PMC model; MM* model; Regular graphs; Fault diagnosability (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:334:y:2018:i:c:p:295-310 DOI: 10.1016/j.amc.2018.04.014 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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