Connectivity and diagnosability of the complete Josephus cube networks under h-extra fault-tolerant model

The h-extra connectivity and the h-extra diagnosability are key parameters for evaluating the reliability and fault-tolerance of the interconnection networks of the multiprocessor systems, and play an important role in designing and maintaining interconnection networks. Recently, various self-diagnostic models have emerged to assess the fault-tolerance in interconnection networks. These interconnection networks are typically expressed by a connected graph G(V, E ). For a non- complete graph G and h >= 0, the h-extra cut signifies a vertex subset R of G , whose removal results in G - R disconnected, with each remaining component containing at least h + 1 vertices. And the h-extra connectivity of G is defined as the minimum cardinality of all h-extra cuts of G . The h-extra diagnosability for a graph G denotes the maximum number of detectable faulty vertices when focusing on these h-extra faulty sets only. The complete Josephus cube CJCn, a variant of Q n , exhibits superior properties compared to hypercube Q n , and also boasts higher connectivity. In this study, with the help of the exact value of the h-extra connectivity of CJCn, the explicit expression of h-extra diagnosability of CJCn under both the PMC model for n >= 5 and 1 <= h <= [ n -3 2 j and the MM* model for n >= 5 and 2 <= h <= [ n -3 2 j are identified to share the same value (h + 1)n - ( h -1 ) + 1. 2