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 S-n(2). Then we propose the upper bound of the {1, 2, 3}-good-neighbor diagnosability of S-n(2), under the MM* model. Moreover, we show that when deleting two indistinguishable good-neighbor faulty vertex-sets from S-n(2), 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 S-n(2), and prove that the lower and upper bounds of the {1, 2, 3}-good-neighbor diagnosability of S-n(2) are accurate. (C) 2020 Elsevier B.V. All rights reserved.