Conditional fault tolerance of arrangement graphs

a r t i c l e i n f o a b s t r a c t 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 κ 1 (A n,k) = (2k − 1)(n − k) − 1 and κ 2 (A n,k) = (3k − 2)(n − k) − 2, respectively.