On Conditional Edge Connectivity Of Two Networks

Using a connected graph to study the underlying topology of an interconnection network has been widely accepted and applied by engineering technicians and computer scientists. When the topology of a network is modeled by a graph, the edge connectivity is an important measurement for reliability and fault tolerance of the network, which can correctly reflects the fault tolerance of the small network, but for the large-scale network, it always underestimates the resilience. With the development of multiprocessor systems, it is necessary to improve the concept of traditional edge connectivity.This dissertation deals with the generalized concept of edge connectivity, k-restricted edge connectivity, super k-restricted edge connectivity and edge fault tolerance of a graph with respect to super k-restricted edge connectivity. We focus on the hypercube and folder hypercube about the k-restricted edge connectivity when k is1,2,3and determine the value of the relevant edge fault tolerance. Using known results, we obtain the following main results:for hypercube Qn, the edge fault tolerances about super edge connectivity with n≥4, super restricted edge connectivity with n≥5and super3-restricted edge connectivity with n≥6are all n-1; for fold hypercube FQn, the edge fault tolerances about super edge connectivity with n≥3, super restricted edge connectivity with n≥2and super3-restricted edge connectivity with n≥5are all n.