Fault tolerance analysis of hierarchical folded cube

Abstract

For the purpose of more accurate reliability of interconnection networks, the g-extra connectivity has been proposed by Fàbrega et al. [Discrete Mathematics 155 (1996) 49–57]. Given a graph G and a positive integer g, the g-extra connectivity of G, say κo(g)(G), is the minimum cardinality of a vertex subset V(S) such that G−S is disconnected and every remaining component has at least g+1 vertices. The g-extra diagnosability of G, denoted by t˜g(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. In this paper, we first determine κo(g)(HFQ(n))=(g+1)n−(g2)+2 for n≥4, 0≤g≤n−4, where HFQ(n) is the n-dimensional hierarchical folded cube. Moreover, we establish t˜g(HFQ(n))=(g+1)(n+1)−(g2)+1 under the PMC model (n≥4, 1≤g≤n−4) and under the MM* model (n≥7, 1≤g≤n−34), respectively.