The Local Diagnosability of Folded Hypercubes with Conditional Faulty Edges Under the PMC Model

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 the n-dimensional folded hypercube FQ(n)(n >= 4) under the PMC model. We prove that FQn-F keeps the strong local diagnosability property even if it has the set F of (n-1) faulty edges and n-1 is maximum number of faulty edges. Secondly, we study the diagnosability of FQ(n)(n >= 5 and n is odd) with conditional faulty edges under the PMC model. We prove that FQn-F keeps strong local diagnosability property even if it has the set F of (3n-4) faulty edges, provided that each vertex of FQ(n)-F is incident with at least two fault-free edges, where 3n-4 is maximum number of faulty edges. Finally, we prove that FQ(n)-F keeps strong local diagnosability property no matter how many edges are faulty, provided that each vertex of FQ(n)-F is incident with at least three fault-free edges.