Unchanging the diameter of k-ary n-cube networks with faulty vertices

The k-ary n-cube is one of the most commonly used interconnection networks for parallel and distributed systems. In this paper, for a k-ary n-cube , we show that if k is even and if k is odd, where is the maximum integer such that the diameter of remains unchanged when arbitrary vertices are faulty. Furthermore, we show that for even k, if the diameter of a faulty with 2n-1 faulty vertices is larger than its fault-free diameter, then all the faulty vertices are adjacent to a certain vertex and there is only one pair of vertices in this such that their distance is equal to the fault diameter. For k-ary n-cubes with odd k, similar results are given.