Subnetworks Reliability Analysis of Complete Transposition Networks

Large scale multiprocessor systems based on interconnection networks (graphs) as underlying topologies, have been widely used in nowdays. Thus, the reliability of interconnection networks will directly affect the stability of multiprocessor systems. The strong Menger connectivity is a significant parameter for the reliability evalution of interconnection networks. A connected graph [Formula: see text] is strong Menger (edge) connected if there are [Formula: see text] internally (edge) disjoint paths joining any two vertices [Formula: see text] and [Formula: see text] in [Formula: see text]. This article studies the strong Menger connectivity of complete transposition networks [Formula: see text] when parts of subnetworks are faulty. Let [Formula: see text] be an [Formula: see text]-dimensional subnetwork of [Formula: see text]. We show that [Formula: see text] is strong Menger (edge) connected, and determine the (edge) connectivity of [Formula: see text] is [Formula: see text].