On g-extra conditional diagnosability of hierarchical cubic networks

Abstract

Connectivity and diagnosability are important parameters in measuring the fault-tolerance and reliability of interconnection networks. Given a graph G and a non-negative integer g, the g-extra connectivity of G, denoted by κg(G), is the minimum cardinality of a set of vertices of G, if it exists, whose deletion disconnects G, and every remaining component has more than g vertices. The g-extra conditional diagnosability tg(G) of a graph G is the maximum value of t such that G is g-extra conditional t-diagnosable. The n-dimensional hierarchical cubic network HCNn was proposed by Ghose and Desai [12] as a hypercube-based topology while preserving its attractive features. For n≥5, we first determine κg(HCNn) for 0≤g≤n+1, then establish tg(HCNn) under the PMC model for 0≤g≤n+1, and tg(HCNn) under the MM⁎ model for 0≤g≤n−13, respectively.