Reliability evaluation of complete cubic networks

Abstract

Fault diagnostic analysis is extremely important for interconnection networks. Given a graph G and a positive integer g, the g-extra connectivity of G (denoted by ) is the minimum cardinality of a subset S of such that G−S is disconnected and every remaining component has at least g + 1 vertices. The g-extra diagnosability of G (denoted by ), 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. The t/k-diagnosis strategy can detect up to t faulty vertices which might include at most k misdiagnosed vertices. In this paper, we first determine for , , where is an n-dimensional complete cubic network, which generalises the hierarchical cubic network. Moreover, we establish under the PMC model (, ) and under the MM* model (, ), respectively. Furthermore, we show that is -diagnosable under the PMC model. As a consequence, we also derive the related results of the n-dimensional hierarchical cubic network .