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 RhRh-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 RhRh-connectivity of the (n,k)(n,k)-arrangement graph An,kAn,k for h=1h=1 and h=2h=2, and determines that κ1(An,k)=(2k−1)(n−k)−1κ1(An,k)=(2k−1)(n−k)−1 and κ2(An,k)=(3k−2)(n−k)−2κ2(An,k)=(3k−2)(n−k)−2, respectively.

► In this study we derive conditional connectivity of arrangement graphs, which is stronger than the traditional connectivity.
► This fault tolerance analysis of arrangement graphs is useful in evaluate the fault diagnosability.
► The method avoids the traditional induction on two parameters.