Super Connectivity And Pessimistic Diagnosability Research In The Exchanged Corssed Cubes

The connectivity is an important parameter to measure stability and fault-tolerance of the interconnection network. The Exchanged Crossed cubes, simply, expressed as ECQ(s,t),is a variant of the hypercube, whose natures are super to the hypercube, such as smaller radius and fewer links. It is proved that the connectivity and the edge-connectivity of ECQ(s,t) are s+1(s?t). Thus, it proves that the super connectivity and the super edge-connectivity of ECQ(s,t) are 2s (s?t),that is, at least 2s vertices(resp.2s edges) of ECQ(s,t) are removed to get a disconnected graph that contains no isolated vertex. When ECQ(s,t) is used to model the topological structure of a large-scale parallel processing system, these results can provide more accurate measurements for reliability and fault tolerance of the system.The degree of diagnosability of an interconnection network is an important standard to measure the stability and fault-tolerance of the interconnection network. The PMC model is regarded as important system-level diagnosis model. The precise one-step tp-diagnosis strategy and the pessimistic one-step t1/t1 -diagnosis strategy are most popular system-level diagnosis strategy. The Exchanged Crossed cubes, simply, expressed as ECQ, is a variant of the hypercube, whose natures are super to the hypercube, such as smaller radius and fewer links. After analysis and studying the topological property of the ECQ, it is proved that ECQ is s+1-diagnosable and 2s/2s-diagnosable respectively under the precise one-step strategy and the pessimistic one-step strategy by using the PMC model. Based on this, ECQ has high fault-tolerant computing performance.