A unified approach to reliability and edge fault tolerance of cube-based interconnection networks under three hypotheses

The topological structures of the interconnection networks of some parallel and distributed systems are designed as n -dimensional hypercube Q n or n -dimensional folded hypercube F Q n with N = 2 n processors. For integers 0 ≤ k ≤ n - 1 , let P 1 k , P 2 k and P 3 k be the property of having at least k neighbors for each processor, containing at least 2 k processors and admitting average neighbors at least k , respectively. P -conditional edge-connectivity of G , λ ( P , G ) , is the minimum cardinality of faulty edge-cut, whose malfunction divides this network into several components, with each component satisfying the property of P . For each integer 0 ≤ k ≤ n - 1 , and 1 ≤ i ≤ 3 , this paper offers a unified method to investigate the P i k -conditional edge-connectivity of Q n and F Q n . Exact value of P i k -conditional edge-connectivity of Q n , λ ( P i k , Q n ) , is ( n - k ) 2 k , and that of P i k -conditional edge-connectivity of F Q n , λ ( P i k , F Q n ) , is ( n - k + 1 ) 2 k . Our method generalizes the result of Guo and Guo in [The Journal of Supercomputing, 2014, 68:1235-1240] and the previous other results.