The Conditional Diagnosability with g-Good-Neighbor of Exchanged Hypercubes

A network's diagnosability is the maximum number of faulty vertices that the network can discriminate solely by performing mutual tests among the vertices. It is an important measure of a network's robustness. The g-good-neighbor conditional diagnosability is the maximum cardinality of g-good-neighbor conditional fault-set that the system is guaranteed to identify. The g-good-neighbor conditional diagnosability of EH(s,t) under the PMC model has been proposed by Liu et al. [Liu, X., Yuan, J. and Ma, X. (2014) The g-good-neighbor conditional diagnosability of the exchange hypercube under the PMC model. J. Taiyuan Univ. Sci. Technol., 35, 390-393]. However, the method by Liu et al. [Liu, X., Yuan, J. and Ma, X. (2014) The g-good-neighbor conditional diagnosability of the exchange hypercube under the PMC model. J. Taiyuan Univ. Sci. Technol., 35, 390-393] is too complicated to follow, and it is not complete. We will propose a complete method to establish the g-good-neighbor conditional diagnosability of EH(s, t) under the PMC model by optimizing the structure of the proof in [Liu, X., Yuan, J. and Ma, X. (2014) The g-good-neighbor conditional diagnosability of the exchange hypercube under the PMC model. J. Taiyuan Univ. Sci. Technol., 35, 390-393] and adding the missing case. Also we add a ratio in a table to represent the probability that a faulty set with size s contains all neighbors of any vertex, which is very low. Moreover, we mainly establish the g-good-neighbor conditional diagnosability for exchanged hypercube EH(s, t) under the comparison model.