Panconnectivity and edge-pancyclicity of k-ary n-cubes with faulty elements

The class of k-ary n-cubes represents the most commonly used interconnection topology for parallel and distributed computing systems. In this paper, we investigate the fault-tolerant capabilities of the k-ary n-cubes for odd integer k with respect to the panconnectivity and pancyclicity. By studying first the fault panconnectivity of two-dimensional torus networks and then using an induction argument, we prove that in a k-ary n-cube Qnk with odd k≥3, every pair of healthy vertices of Qnk are connected by fault-free paths of lengths from n(k−1)−1 to |V(Qnk−F)|−1 and every healthy edge is contained in fault-free cycles of lengths from n(k−1) to |V(Qnk−F)| for any set F of faulty elements (vertices and/or edges) with |F|≤2n−3. Finally, examples show that our results are best possible in some sense.