Restricted connectivity and good-neighbor diagnosability of split-star networks.

The restricted connectivity and the g-good-neighbor diagnosability are two important indicators of the robustness for a multi-processor system in presence of failing processors. The g-good-neighbor diagnosability of a graph guarantees that the number of fault-free neighbors of every fault-free vertex is greater or equal to g in the graph. We first establish the 3-restricted connectivity of an n-dimensional split-star network Sn2. Then we propose the upper bound of the {1,2,3}-good-neighbor diagnosability of Sn2 under the MM* model. Moreover, we show that when deleting two indistinguishable good-neighbor faulty vertex-sets from Sn2, the remaining connected subgraph has no isolated vertex. Furthermore, we give a complete proof for the lower bound of the {1,2,3}-good-neighbor diagnosability of Sn2, and prove that the lower and upper bounds of the {1,2,3}-good-neighbor diagnosability of Sn2 are accurate.