The Local Diagnosability of a Class of Cayley Graphs with Conditional Faulty Edges Under the PMC Model

Abstract

Abstract The diagnosability of a multiprocessor system is of great significance in measuring the reliability and faulty tolerance of interconnection networks. In this paper, we firstly study the diagnosability of a class of Cayley graphs $Cay(H_n,S_n)$ under the PMC model. We prove that $Cay(H_n,S_n)-F$ keeps the strong local diagnosability property even if it has the set $F$ of $(m-2)$ faulty edges and $m-2$ is maximum number of faulty edges, where $m$ is the regular degree of $Cay(H_n,S_n)$. Secondly, we study the diagnosability of $Cay(H_n,S_n)$ with conditional faulty edges under the PMC model. We prove that $Cay(H_n,S_n)-F$ keeps strong local diagnosability property even if it has the set $F$ of $(3m-10)$ faulty edges, provided that each vertex of $Cay(H_n,S_n)-F$ is incident with at least two fault-free edges, where $3m-10$ is maximum number of faulty edges. Finally, we prove that $Cay(H_n,S_n)-F$ keeps strong local diagnosability property no matter how many edges are faulty, provided that each vertex of $Cay(H_n,S_n)-F$ is incident with at least four fault-free edges.