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 .