Some Properties of the <i>g</i>-Good-Neighbor (<i>g</i>-Extra) Diagnosability of a Multiprocessor System

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