Reliability Analysis of the Generalized Exchanged Hypercube

Abstract

Let [Formula: see text] be a non-complete graph, a subset [Formula: see text] is called a [Formula: see text]-component cut of [Formula: see text], if [Formula: see text] is disconnected and has at least [Formula: see text] components. The cardinality of the minimum [Formula: see text]-component cut is the [Formula: see text]-component connectivity of [Formula: see text] and is denoted by [Formula: see text]. The [Formula: see text]-component connectivity is a natural extension of the classical connectivity. As an application, the [Formula: see text]-component connectivity can be used to evaluate the reliability and fault tolerance of an interconnection network structure based on a graph model. In a previous work, E. Cheng et al. obtained the [Formula: see text]-component connectivity of the generalized exchanged hypercube [Formula: see text] for [Formula: see text] and [Formula: see text]. In this paper, we continue the work and determine that [Formula: see text] for [Formula: see text]. Moreover, we show that every optimal [Formula: see text]-component cut of [Formula: see text] is trivial for [Formula: see text] and [Formula: see text].