The 4-Set Tree Connectivity of Folded Hypercube

Abstract

The [Formula: see text]-set tree connectivity, as a natural extension of classical connectivity, is a very important index to evaluate the fault-tolerance of interconnection networks. Let [Formula: see text] be a connected graph and a subset [Formula: see text], an [Formula: see text]-tree of graph [Formula: see text] is a tree [Formula: see text] that contains all the vertices of [Formula: see text] and [Formula: see text]. Two [Formula: see text]-trees [Formula: see text] and [Formula: see text] are internally disjoint if and only if [Formula: see text] and [Formula: see text]. The cardinality of maximum internally disjoint [Formula: see text]-trees is defined as [Formula: see text], and the [Formula: see text]-set tree connectivity is defined by [Formula: see text]. In this paper, we show that the [Formula: see text]-set tree connectivity of folded hypercube when [Formula: see text], that is, [Formula: see text], where [Formula: see text] is folded hypercube for [Formula: see text].