On g-extra conditional diagnosability of hierarchical cubic networks

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 kappa(g)(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 t(g)(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 Kg(HCNn) for 0 <= g <= n + 1, then establish t(g)(HCNn) under the PMC model for 0 <= g <= n + 1, and t(g)(HCNn) under the MM* model for 0 <= g <= n-1/3. respectively. (C) 2019 Elsevier B.V. All rights reserved.