The Cyclic Diagnosability Of Hypercubes Under The PMC Model And The MM* Model

Abstract

Abstract Motivated by a multitude of practical applications, many distinct vulnerability parameters of multiprocessor systems have been explored. Traditional connectivity and diagnosability are undoubtedly the most well investigated of these metrics, but often fail to capture the most subtle differences of a multiprocessor system. Subsequently, it is necessary to take into account the minimum degree of components, the size of components or the number of components. However, the structure of the components is ignored in these circumstances. In this work, we propose a novel diagnostic strategy based on cyclic connectivity, namely the cyclic diagnosability. The cyclic diagnosability, denoted by $ct(G)$, is the maximum size of the faulty vertex set $F$ of $G$ such that the self-diagnosable system $G$ can identify all the vertices in $F$ under the condition that at least two connected components of $G-F$ contain a cycle. Furthermore, we investigate the cyclic diagnosability of hypercube $Q_{n}$ under the PMC model and the MM* model, and show that $ct(Q_{n})=5n-10$ for $n\geq 7$.