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 \(G\!E\!X(s,t)\) and present the lower (upper) bounds of the \(R_g\) -conditional diagnosability of \(G\!E\!X(s,t)\) 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.
