Abstract
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.
Acknowledgement
This work is supported in part by the National Natural Science Foundation of China (61370001,61303020,U1304601), the Doctoral Fund of Ministry of Education of China (20111401110005) and the Natural Science Foundation of Shanxi Province (2013021018-3).