Conditional fault tolerance of arrangement graphs

Fault tolerance is especially important for interconnection networks, since the growing size of the networks increases its vulnerability to component failures. A classic measure for the fault tolerance of a network in the case of vertex failures is its connectivity. Given a network based on a graph G and a positive integer h, the R^h-connectivity of G is the minimum cardinality of a set of vertices in G, if any, whose deletion disconnects G, and every remaining component has minimum degree at least h. This paper investigates the R^h-connectivity of the (n,k)-arrangement graph A"n","k for h=1 and h=2, and determines that @k^1(A"n","k)=(2k-1)(n-k)-1 and @k^2(A"n","k)=(3k-2)(n-k)-2, respectively.