Edge-bipancyclicity of the k-ary n-cubes with faulty nodes and edges

The k-ary n-cube has been one of the most popular interconnection networks for massively parallel systems. In this paper, we investigate the edge-bipancyclicity of k-ary n-cubes with faulty nodes and edges. It is proved that every healthy edge of the faulty k-ary n-cube with fv faulty nodes and fe faulty edges lies in a fault-free cycle of every even length from 4 to kn − 2fv (resp. kn − fv) if k ⩾ 4 is even (resp. k ⩾ 3 is odd) and fv + fe ⩽ 2n − 3. The results are optimal with respect to the number of node and edge faults tolerated.