Embedded Edge Connectivity of Alternating Group Networks

The topological structure of almost all interconnection networks is constructed in a recursive manner. For an [Formula: see text]-dimensional recursive network [Formula: see text] can be constructed by some different copies of [Formula: see text] by adding some edges among them. The reliability and stability of recursive networks are usually measured by the [Formula: see text]-embedded edge connectivity. For an [Formula: see text]-dimensional recursive network [Formula: see text], the [Formula: see text]-embedded edge connectivity of [Formula: see text], denoted by [Formula: see text], is the minimum size of edges whose removal disconnects [Formula: see text] and each vertex in the resulting network is in a [Formula: see text]-dimensional subnetwork [Formula: see text]. The [Formula: see text]-dimensional alternating group network [Formula: see text] is a typical recursive network. In this paper, we show that [Formula: see text] for [Formula: see text] and [Formula: see text].