Diagnosability of a multiprocessor system is one important study topic. In 2012, Peng et al. proposed\na measure for fault tolerance of the system, which is called the g-good-neighbor diagnosability\nthat restrains every fault-free node containing at least g fault-free neighbors. In 2015, Zhang et al.\nproposed a measure for fault diagnosis of the system, namely, g-extra diagnosability, which\nrestrains that every fault-free component has at least g 1 fault-free nodes. In this paper, we\nobtain some properties of the g-good-neighbor (g-extra) diagnosability of the system and give the\ng-good-neighbor (g-extra) diagnosability of some graphs under the PMC model and MM* model.
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