Hybrid fault diagnosis capability analysis of regular graphs under the PMC model

Abstract

Diagnosabilty is an important metric to the capability of fault identification for multiprocessor systems. However, most researches on diagnosability focus on vertex fault. In real circumstances, not only vertex faults take place but also malfunctions may arise. In this paper, we study the diagnosability of k-regular 2-cn graph with missing edges. Let $F_e$ be a set of missing edges in graph G with $|F_e|\le k-5$. We prove that the diagnosability of $G-F_e$ is at most $\delta (G-F_e)$ for $k\ge 5$. Furthermore, we obtain that the worst-case diagnosability (h-edge tolerable diagnosability), denoted by $t_h^e\left(G\right)$, is maximum number of faulty nodes that a system G can guarantee to locate when the number of faulty links does not exceed h. As applications, the diagnosabilities of many networks with missing edges are determined under the PMC model.

Keywords:

• Diagnosability
• hybrid diagnosability
• PMC model
• regular graph
• application

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research is supported by NSFC - National Natural Science Foundation of China (Nos. 11531011).