Persistence of Hybrid Diagnosability of Regular Networks Under Testing Diagnostic Model

Abstract

Diagnosability is an important metric to fault tolerance and reliability for multiprocessor systems. However, plenty of research on fault diagnosability focuses on node failure. In practical scenario, not only node failures take place but also link malfunctions may arise. In this work, we investigate the diagnosability of general regular networks with failing nodes as well as missing malfunctional links. Let $S$ be a set of the missing links and broken-down nodes. We first prove that the diagnosability of the survival graph $G\setminus S$ persists $\delta (G\setminus S)$ under the PMC model (Preparata, F.P., Metze, G. and Chien, R.T. (1967) On the connection assignment problem of diagnosable systems. IEEE Trans. Electron. Comput., EC-16, 848–854) for a $t$ -regular and $t$ -connected triangle-free network $G$ subject to $|S|\leq t-1$ and $|V(G)|\geq 3t-2$ ( $t\geq 3$ ). Furthermore, we determine the diagnosability of $G\setminus S$ for some kinds of extensively explored $t$ -regular networks with triangles subject to $|S|\leq t-1$ ( $t\geq 3$ ).