Diagnosability and hybrid diagnosability of some classes of graphs under the BPMC model

Abstract

Diagnosability is an important metric to the capability of fault identification for multiprocessor systems. For considering system-level diagnosis, Lian and Zhou proposed the (f1,f2)-BPMC model which is a novel testing model and is the generalization of the PMC model and the BGM model. For measuring the fault diagnosis capability of a multiprocessor system with faulty links, Zhu et al. (2019) introduced the h-edge tolerable diagnosability which is the generalization of the concept of the traditional diagnosability. In this paper, we discuss the diagnosability of a graph under the (f1,f2)-BPMC model, the h-edge tolerable diagnosability of a k-regular graph (k≥6) for 0≤h≤k and 1≤cn(G)≤⌊k3⌋−1 under the PMC model and the MM⁎ model, and the h-edge tolerable diagnosability of an f1-regular graph (f1≥3) for 0≤h≤f1 under the (f1,f2)-BPMC model if N(x)∩N(y)=∅ for any (x,y)∈E(G) and N(u)≠N(v) for any two distinct vertices u,v∈V(G). Some previous results in (Lian et al. (2020) [17]) and (Lin and Teng (2014) [14]) are extended.