The 4-component connectivity of alternating group networks

The l-component connectivity (or l-connectivity for short) of a graph G, denoted by kappa(l)(G), is the minimum number of vertices whose removal from G results in a disconnected graph with at least l components or a graph with fewer than l vertices. This generalization is a natural extension of the classical connectivity defined in term of minimum vertex-cut. As an application, the l-connectivity can be used to assess the vulnerability of a graph corresponding to the underlying topology of an interconnection network, and thus is an important issue for reliability and fault tolerance of the network. So far, only a little knowledge of results have been known on l-connectivity for particular classes of graphs and small l's. In a previous work, we studied the l-connectivity on n-dimensional alternating group networks AN(n) and obtained the result kappa(3)(AN(n)) = 2n - 3 for n >= 4. In this sequel, we continue the work and show that kappa(4) (AN(n)) = 3n - 6 for n >= 4. (C) 2018 Elsevier B.V. All rights reserved.