The upper and lower bounds of Rg-conditional diagnosability of networks

Abstract

The Rg-conditional diagnosability is a new generalization of conditional diagnosability, which restricts that every vertex contains at least g fault-free neighbors. Recently, Wang et al. investigated the Rg-conditional diagnosability of the n-dimensional hypercube under the PMC model, and showed a lower bound of its Rg-conditional diagnosability. In this paper, we investigate the Rg-conditional diagnosability of general networks under the PMC model, and present the lower and upper bounds of Rg-conditional diagnosability of networks under some reasonable conditions. Applying our results, an improved lower bound of Rg-conditional diagnosability of hypercubes and the lower and upper bounds of the Rg-conditional diagnosability of exchanged hypercubes are given.