Embedding paths and cycles in 3-ary n-cubes with faulty nodes and links

The k-ary n-cube, denoted by image, is one of the most important interconnection networks for parallel computing. In this paper, we consider the problem of embedding cycles and paths into faulty 3-ary n-cubes. Let F be a set of faulty nodes and/or edges, and image. We show that when image, there exists a cycle of any length from 3 to image in image. We also prove that when image, there exists a path of any length from image to image between two arbitrary nodes in image. Since the k-ary n-cube is regular of degree image, the fault-tolerant degrees image and image are optimal.