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

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 the [Formula: see text]-dimensional folded hypercube [Formula: see text] under the PMC model. We prove that [Formula: see text] keeps the strong local diagnosability property even if it has the set [Formula: see text] of [Formula: see text] faulty edges and [Formula: see text] is maximum number of faulty edges. Secondly, we study the diagnosability of [Formula: see text] [Formula: see text] and [Formula: see text] is odd) with conditional faulty edges under the PMC model. We prove that [Formula: see text] keeps strong local diagnosability property even if it has the set [Formula: see text] of [Formula: see text] faulty edges, provided that each vertex of [Formula: see text] is incident with at least two fault-free edges, where [Formula: see text] is maximum number of faulty edges. Finally, we prove that [Formula: see text] keeps strong local diagnosability property no matter how many edges are faulty, provided that each vertex of [Formula: see text] is incident with at least three fault-free edges.