Reliability of (n,k)-star network based on g-extra conditional fault

Abstract

In the wake of rapid development of multiprocessor systems, fault tolerance of processors plays an even more vital role in measuring the reliability of a multiprocessor system. The g-extra connectivity of a multiprocessor system modeled by graph G, denoted by κo(g)(G), is the minimum number of nodes whose deletion will disconnect the network and every remaining component has more than g vertices. The g-extra conditional diagnosability of multiprocessor system G, denoted by tg˜(G), is the maximum number of faulty vertices that the system can guarantee to identify under the condition that every fault-free component contains at least g+1 vertices. Only a few achievements have been established on κo(g)(G) for some special graphs with small g. In this paper, we first determine that the g-extra connectivity of (n,k)-star network Sn,k is κo(g)(Sn,k)=n+g(k−2)−1 for 2≤k≤n−1 and 0≤g≤n−k and then show that the g-extra conditional diagnosability of Sn,k under the PMC model (n≥4, 2≤k≤n−1 and 1≤g≤n−k) and the MM* model (n≥6, 3≤k≤n−3 and 1≤g≤min⁡{n−k+14,k−2}) is tg˜(Sn,k)=n+g(k−1)−1, respectively. Meanwhile, we also show that Sn,k is (n+m(k−2)−1)/m-diagnosable under the pessimistic diagnostic strategy. As by-products, we derive the g-extra conditional diagnosability of n-dimensional star graph Sn (n≥4, g=1) and n-dimensional alternating group network ANn (n≥4, 1≤g≤2) under the PMC model.