The Component (Edge) Connectivity of Round Matching Composition Networks

The vertex (edge) connectivity has been regularly used to measure the fault tolerance and reliability of interconnection networks, while it has defects in the assumption that all neighbors of one node will fail concurrently. To overcome this deficiency, some new generalizations of traditional connectivity have been suggested to quantize the size or the number of the connected components of the survival graph. The [Formula: see text]-component (edge) connectivity, one generalization of vertex (edge) connectivity, has been proposed to characterize the vulnerability of multiprocessor systems based on the number of components of the survival graph. In this paper, we determine the [Formula: see text]-component (edge) connectivity of a family of networks, called the round matching composition networks [Formula: see text], which are a class of networks composed of [Formula: see text] ([Formula: see text]) clusters with the same order, linked by [Formula: see text] perfect matchings. By exploring the combinatorial properties and fault-tolerance of [Formula: see text], we establish the [Formula: see text]-component (edge) connectivity [Formula: see text] for [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text].