Reliability Evaluation of Generalized Exchanged X-Cubes Based on the Condition of g-Good-Neighbor

In the cloud computing environment with massive information services and decision-making resources, the accuracy and reliability of information are more important than previous single closed systems. Therefore, ensuring the reliability of information and the stable operation of the system are the core problems in the research fields such as the Internet Plus and the Internet of Things. The connectivity and diagnosability are two important measures for the fault tolerance of multiprocessor systems. The g-good-neighbor conditional connectivity (Rg-connectivity) is the minimum number of nodes that make the graph disconnected, and each node has at least g neighbors in every remaining component. The g-good-neighbor conditional diagnosability (g-GNCD) is the maximum number of faulty processors that has been correctly identified in a system, and any fault-free processor has no less than g fault-free neighbors. Exchanged X-cubes are a class of irregular networks, obtained by deleting links from hypercubes and some variant networks of hypercubes (X-cubes). They not only combine the advantages of X-cubes but also reduce the interconnection complexity. Exchanged X-cubes classify its nodes into two different classes clusters with a unique connecting rule. In this paper, we propose the generalized exchanged X-cubes framework so that architecture can be constructed by different connecting rules. Furthermore, we study the Rg-connectivity and g-GNCD of generalized exchanged X-cubes under the PMC and MM models. As applications, the Rg-connectivity and g-GNCD of generalized exchanged hypercubes, dual-cube-like networks, generalized exchanged crossed cubes, and locally generalized exchanged twisted cubes are determined, respectively.