The Partial Diagnosability of Interconnection Networks Under the Strong Hybrid MM* Model

The diagnosability analysis of interconnection networks constitutes a fundamental challenge in faulty-tolerant computing systems, especially in the presence of faulty edges and faulty vertices. The fault diagnosis models PMC [8] and MM* [9] for the networks with faulty vertices have been proposed and extensively investigated. When the network contains faulty edges simultaneously, based on the PMC model, Zhu et al. [20] and Yuan et al. [15] gave the definition of consistency and determined the [Formula: see text]-edge restricted vertex-diagnosability and the [Formula: see text]-vertex restricted edge-diagnosability. These two diagnosabilities were termed partial diagnosabilities under the HPMC model. Then, by combining the consistency with MM* model, Tan et al. [10] defined the HMM* model and determined the partial diagnosability for [Formula: see text]-dimensional hypercubes. In this paper, in order to further satisfy the characteristic of the MM* model, we proposed the strong consistency and gave the SHMM* model, accordingly. Then, considering the importance of the triangle-free network where each vertex has the same number of neighbors, we investigated the partial diagnosability under the SHMM* model for these networks and observed that, compared with HPMC and HMM* models, the diagnosability of the network can be significantly improved. Furthermore, we applied our results to several well-known interconnection networks, including BC networks, folded hypercubes and star graphs.