Reliability Assessment of Multiprocessor System Based on Exchanged Crossed Cube Networks

With the increasingly widespread application of multiprocessor systems, some processors in multiprocessor systems are inevitably prone to malfunctions. The reliability and effectiveness of the system are key issues. As a standard for measuring system fault tolerance, connectivity, and edge connectivity have many drawbacks. Therefore, Haray proposed conditional connectivity by restricting the connected components in disconnected subgraphs $G-F$ to satisfy certain properties, where $G$ and $F$ represent the interconnection network and its set of faulty vertices, respectively. Restricted connectivity is a special type of conditional connectivity. Exchanged crossed cube, as a deformation of hypercube, has more favorable properties, such as smaller diameter, smaller link size, and lower cost. We prove that the 2-restricted connectivity of the exchanged crossed cubes $\text{ECQ}(s,t)$ is $4s-4$ for $2\le s\le t$.