Component Fault Diagnosability of Hierarchical Cubic Networks

The fault diagnosability of a network indicates the self-diagnosis ability of the network, thus it is an important measure of robustness of the network. As a neoteric feature for measuring fault diagnosability, the r-component diagnosability ctr(G) of a network G imposes the restriction that the number of components is at least r in the remaining network of G by deleting faulty set X, which enhances the diagnosability of G. In this article, we establish the r-component diagnosability for n-dimensional hierarchical cubic network HCNn, and we show that, under both PMC model and MM∗model, the r-component diagnosability of HCNn is rn-½(r-1)r+1 for n≥ 2 and 1≤ r≤ n-1. Moreover, we introduce the concepts of 0-PMC subgraph and 0-MM∗subgraph of HCNn. Then, we make use of 0-PMC subgraph and 0-MM∗subgraph of HCNn to design two algorithms under PMC model and MM∗model, respectively, which are practical and efficient for component fault diagnosis of HCNn. Besides, we compare the r-component diagnosability of HCNn with the extra conditional diagnosability, diagnosability, good-neighbor diagnosability, pessimistic diagnosability, and conditional diagnosability, and we verify that the r-component diagnosability of HCNn is higher than the other types of diagnosability.