The 2-good-neighbor (2-extra) diagnosability of alternating group graph networks under the PMC model and MM* model

Abstract

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 2016, Zhang et al. proposed a new measure for fault diagnosis of the system, namely, the g-extra diagnosability, which restrains that every fault-free component has at least (g+1) fault-free nodes. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph network ANn has many good properties. In this paper, we obtain that (a) the 2-good-neighbor diagnosability of ANn is 3n−7 for n ≥ 4 under the PMC model and MM* model; (b) the 2-extra diagnosability of ANn is 3n−7 for n ≥ 4 under the PMC model, and the 2-extra diagnosability of ANn is 3n−7 for n ≥ 5 under the MM* model. These results are optimal with respect to 2-extra diagnosability of ANn.