Edge-bipancyclicity in conditional edge-faulty k-ary n-cubes

The class of k-ary n-cubes represents the most commonly used interconnection topology for parallel and distributed computing systems. In this paper, we consider the faulty k-ary n-cube with even k ≥ 4 and n ≥ 2 such that each vertex of the k-ary n-cube is incident with at least two healthy edges. Based on this requirement, we investigate the fault-tolerant capabilities of the k-ary n-cube with respect to the edge-bipancyclicity. We prove that in the k-ary n-cube Qnk, every healthy edge is contained in fault-free cycles of even lengths from 6 to |V(Qnk)|, even if the Qnk has up to 4n − 5 edge faults and our result is optimal with respect to the number of edge faults tolerated.