The Pessimistic Diagnosability of Folded Petersen Cubes

Abstract

Diagnosability is an important metric parameter for measuring the reliability of multiprocessor systems. The pessimistic diagnosis strategy is a classic diagnostic model based on the PMC model. The class of folded Petersen cubes, denoted by $\text{FP}{Q}_{n,k}$ , where $n,k\ge 0$ and $\left(n,k\right)\ne \left(0,0\right)$ , is introduced as a competitive model of the hypercubes, which is constructed by iteratively applying the Cartesian product operation on the hypercube $Q_n$ and the Petersen graph $P$ . In this paper, by exploring the structural properties of the folded Petersen cubes $\text{FP}{Q}_{n,k}$ , we first prove that $\text{FP}{Q}_{n,k}$ is $\left(n+3k\right)$ diagnosable under the PMC model. Then, we completely derive that the pessimistic diagnosability of $\text{FP}{Q}_{n,k}$ is $2n+6k-2$ under the PMC model. Furthermore, the diagnosability and the pessimistic diagnosability of the class of folded Petersen cubes, including the hypercube, folded Petersen graph, and hyper Petersen graph, are obtained.