The Generalized Connectivity of Data Center Networks

The generalized [Formula: see text]-connectivity of a graph [Formula: see text] is a parameter that can measure the reliability of a network [Formula: see text] to connect any [Formula: see text] vertices in [Formula: see text], which is a generalization of traditional connectivity. Let [Formula: see text] and [Formula: see text] denote the maximum number [Formula: see text] of edge-disjoint trees [Formula: see text] in [Formula: see text] such that [Formula: see text] for any [Formula: see text] and [Formula: see text]. For an integer [Formula: see text] with [Formula: see text], the generalized [Formula: see text]-connectivity of a graph [Formula: see text] is defined as [Formula: see text] and [Formula: see text]. Data centers are essential to the business of companies such as Google, Amazon, Facebook and Microsoft et al. Based on data centers, the data center networks [Formula: see text], introduced by Guo et al. in 2008, have many desirable properties. In this paper, we study the generalized [Formula: see text]-connectivity of [Formula: see text] and show that [Formula: see text] for [Formula: see text] and [Formula: see text].