Reliability of arrangement networks in terms of the h-restricted edge connectivity

Abstract

The h-restricted edge connectivity λh is an important parameter to measure the reliability of massive parallel computing system. The λh of G is the minimum cardinality of a set of edges in G, if any, whose deletion disconnects G, and every remaining component has minimum degree at least h. The arrangement graph is a generalization of the star graph, but its order is more flexible than that of the star graph. This paper investigates the h-restricted edge connectivity of the (n,k)-arrangement graph An,k, and determines that λ1(An,k)=2k(n−k)−2, λ2(An,k)=3k(n−k)−6 with k≤n−2.