Structural diagnosability of hypercubes under the PMC and MM* models

Abstract

The fault diagnosability has played an important role in the reliability of the interconnection network. In a network, the states of any two adjacent vertices can usually affect each other, and the neighbor of a faulty vertex is more likely to become faulty. These motivate our study of fault diagnosability from the perspective of some structures instead of basing on individual faulty vertices. Therefore, we introduce a novel measure of diagnosability, called structural diagnosability. Given a specific structure H, the H-structure diagnosability of a network G, denoted by ts(G;H), is the maximum number of pairwise disjoint subnetworks H1,H2,…,Hm in G, such that, for i=1,2,…,m, Hi is isomorphic to H and when all vertices in Hi are faulty, these vertices can be diagnosed correctly. In this paper, we will establish ts(Qn;H) for the n-dimensional hypercube Qn under the PMC model and MM* model, respectively, where H∈{K1,1,K1,2,K1,3,C4}.