On g-good-neighbor conditional connectivity and diagnosability of hierarchical star networks

In this paper, we study the connectivity and diagonosability of n-dimensional hierarchical star network HS, based on the concept of forbidden faulty sets. In a forbidden faulty set, certain nodes cannot be faulty at the same time and this model can better reflect fault patterns in a real system than the existing ones. Under the condition every fault-free node in a network contains at least g fault-free neighbors, the g-good neighbor conditional connectivity is defined as the minimum number of faulty processors whose deletion makes the network disconnected, the g-good neighbor conditional diagnosability t(g)(G) is defined as the maximum number of faulty processors that the network can guarantee to identify solely by performing mutual tests among the processors. We investigate the g-good neighbor conditional connectivity and the g-good-neighbor conditional diagnosability of n-dimensional hierarchical star network HSn. Our results show that the g-good-neighbor conditional connectivity of HSn is (n - g)(g + 1)! - 1 and the g-good-neighbor conditional diagnosability of HS, under the PMC and MM* models is (n - g + 1)(g + 1)! - 1 when 0 <= g <= n - 3, g not equal 2 and n >= 4. In addition, we show the 2-good-neighbor conditional connectivity of HSn is 4n - 8 and the 2-good-neighbor conditional diagnosability of HSn under the PMC and MM* models is 4n - 5 when n >= 4. (C) 2021 Elsevier B.V. All rights reserved.