Component Connectivity of Alternating Group Networks and Godan Graphs

Connectivity is an important index to evaluate the reliability and fault tolerance of a graph. As a natural extension of the connectivity of graphs, the g-component connectivity of a graph G, denoted by c kappa(g)(G), is the minimum number of vertices whose removal from G results in a disconnected graph with at least g components. It is a scientific issue to determine the exact values of c kappa(g)(G) for distinguishing the fault tolerability of networks. However, g-component connectivity of many well-known interconnection networks has not been explored even for small g's. For the n-dimensional alternating group networks AN(n) and n-dimensional godan graphs EA(n), we show that c kappa(5)(AN(n)) = 4n - 8 for n >= 6, and c kappa(g)(EA(n)) = (g - 2)(n - 2) + n for g is an element of{3, 4, 5} and n >= 4.