The 4-component connectivity of alternating group networks

Abstract The l -component connectivity (or l -connectivity for short) of a graph G , denoted by κ 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 A N n and obtained the result κ 3 ( A N n ) = 2 n − 3 for n ⩾ 4 . In this sequel, we continue the work and show that κ 4 ( A N n ) = 3 n − 6 for n ⩾ 4 .