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).