Strong Menger Connectivity of Alternating Group Network Under Subnetwork Failure

The construction of vertex (edge) disjoint paths have been well applied to the study of connectivity, diameter, parallel routing, reliability and fault tolerance of an interconnection network. The Menger-type problem about vertex (edge) disjoint paths in interconnection network has received extensive attention. A connected graph is strong Menger vertex (edge) connected if there exist [Formula: see text] vertex (edge) disjoint paths between any two distinct vertices [Formula: see text] and [Formula: see text] in graph [Formula: see text]. In this work, we determine the strong Menger connectivity of alternating group network ([Formula: see text]) when the genetic subnetwork fails. In detail, we show that [Formula: see text] is strong Menger vertex (edge) connected where [Formula: see text] is isomorphic to [Formula: see text] ([Formula: see text]).