The R-g-conditional diagnosability of international networks

The R-g-conditional diagnosability of a multiprocessor system modeled by a graph G, denoted by t(Rg)(G), is a generalization of conditional diagnosability, which restricts every vertex contains at least g fault-free neighbors. Particularly, the R-1-conditional diagnosability is the conditional diagnosability. The R-g-conditional connectivity of a graph G, denoted by kappa(Rg) (G), is the minimum number of vertices, whose deletion will disconnect the graph and every vertex of G has at least g neighbors in the remaining subgraphs. In this paper, the relationships between the R-g-conditional connectivity of a graph G and its R-g-conditional diagnosability under the PMC and MM* models are explored. We establish the Rg-conditional diagnosability t(Rg) (G) equals kappa(R2g+1) (G) + g under some reasonable conditions, except the R-1-conditional diagnosability of G under the MM* model. Moreover, we show under the MM* model, t(R1) (G) = kappa(R2)(G) with similar conditions. Applying our results, the R-g-conditional diagnosability of the (n, k)-star graphs and the (n, k)-bubble-sort graphs are determined. (C) 2021 Elsevier B.V. All rights reserved.