Hybrid fault g-good-neighbor conditional diagnosability of star graphs

Diagnosability is a vital metric to the capability of fault diagnosis of multiprocessor systems. Some scholars studied the g-good-neighbor conditional diagnosability of multiprocessor systems, these researches only focus on vertex fault. But in real operation, the edge fault is inevitable. Thus, we consider h-edge g-good-neighbor conditional diagnosability. The g-good-neighbor conditional faulty vertex set F satisfies that every fault-free vertex has at least g fault-free neighbors of G-F. The h-edge g-good-neighbor conditional diagnosability is the maximum cardinality of the g-good-neighbor conditional faulty set that the graph is guaranteed to identify when the number of faulty edges does not exceed h. In the paper, we obtain the h-edge g-good-neighbor conditional diagnosability of n-dimensional star graphs under the PMC model and MM* model to be (n - g)(g + 1)! - 1 -h for n = 4, 0 = g = n - 2 and 0 = h = n - 2 - g.

Automated summary

Diagnosability is an important metric for fault diagnosis in multiprocessor systems. Previous studies only focused on vertex faults, but we considered edge faults as well and obtained the h-edge g-good-neighbor conditional diagnosability of n-dimensional star graphs under the PMC and MM* models.