The Structure Fault Tolerance of Alternating Group Networks

The alternating group network [Formula: see text] can be used to model the topology structure of a large-scale parallel network system. In this work, the structure fault tolerance of alternating group networks based on the star and path structures is investigated. For a graph [Formula: see text] and its a connected subgraph [Formula: see text], the [Formula: see text]-structure connectivity [Formula: see text] (resp. [Formula: see text]-substructure connectivity [Formula: see text]) of [Formula: see text] is the cardinality of a minimum family [Formula: see text] whose every element is isomorphic to [Formula: see text] (resp. isomorphic to a subgraph of [Formula: see text]) such that [Formula: see text] is disconnected. Specifically, we determine [Formula: see text] and [Formula: see text] for [Formula: see text].