The g-Good-Neighbor Conditional Diagnosability of k-Ary n-Cubes under the PMC Modeland MM* Model

The diagnosability of a system is defined as the maximum number of faulty processors that the system can guarantee to identify, which plays an important role in measuring of the reliability of multiprocessor systems. In the work of Peng et al. in 2012, they proposed a new measure for fault diagnosis of systems, namely,g-good-neighbor conditional diagnosability. It is defined as the diagnosability of a multiprocessor system under the assumption that every fault-free node contains at leastgfault-free neighbors, which can measure the reliability of interconnection networks in heterogeneous environments more accurately than traditional diagnosability. Thek-aryn-cube is a family of popular networks. In this study, we first investigate and determine theRg-connectivity ofk-aryn-cube for0≤ g≤ n.Based on this, we determine theg-good-neighbor conditional diagnosability ofk-aryn-cube under the PMC model and MM* model fork≥ 4, n≥ 3and0≤ g≤ n.Our study shows theg-good-neighbor conditional diagnosability ofk-aryn-cube is several times larger than the classical diagnosability ofk-aryn-cube.