The Generalized 3-Connectivity of Exchanged Crossed Cube

Abstract

Let [Formula: see text] be a connected graph, and [Formula: see text] with [Formula: see text]. [Formula: see text] refers to the maximum number [Formula: see text] of edge-disjoint trees [Formula: see text] in [Formula: see text] such that [Formula: see text] for distinct [Formula: see text]. The generalized [Formula: see text]-connectivity of [Formula: see text], denoted by [Formula: see text], is defined as the minimum value of [Formula: see text] over all [Formula: see text] with [Formula: see text]. In fact, [Formula: see text] is exactly the traditional connectivity of [Formula: see text]. Exchanged crossed cube [Formula: see text], a variation of hypercube, has better properties than other variations of hypercube. In this work we obtain that [Formula: see text] with [Formula: see text].