Reliability evaluation of generalized exchanged X-cubes under the R_g-conditional restriction

In the realm of multiprocessor systems, the evaluation of interconnection network reliability holds utmost significance, both in terms of design and maintenance. The intricate nature of these systems calls for a systematic assessment of reliability metrics, among which, two metrics emerge as vital: connectivity and diagnosability. The R-g-conditional connectivity is the minimum number of processors whose deletion will disconnect the multiprocessor system and every processor has at least g fault-free neighbors. The R-g-conditional diagnosability is a novel generalized conditional diagnosability, which is the maximum number of faulty processors that can be identified under the condition that every processor has no less than g fault-free neighbors. In this paper, we first investigate the R-g-conditional connectivity of generalized exchanged X-cubes GEX(s , t) and present the lower (upper) bounds of the R-g-conditional diagnosability of GEX(s , t) under the PMC model. Applying our results, the R-g-conditional connectivity and the lower (upper) bounds of R-g-conditional diagnosability of generalized exchanged hypercubes, generalized exchanged crossed cubes, and locally generalized exchanged twisted cubes under the PMC model are determined. Our comparative analysis highlights the superiority of R-g-conditional diagnosability, showcasing its effectiveness in guiding reliability studies across a diverse set of networks.