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 FPQn,k, where n, k ≥ 0 and (n, k) ≠ (0, 0), is introduced as a competitive model of the hypercubes, which is constructed by iteratively applying the Cartesian product operation on the hypercube Qn and the Petersen graph P. In this paper, by exploring the structural properties of the folded Petersen cubes FPQn,k, we first prove that FPQn,k is (n + 3k) diagnosable under the PMC model. Then, we completely derive that the pessimistic diagnosability of FPQn,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.