Panconnectivity and edge-pancyclicity of image-ary image-cubes with faulty elements Original Research Article

The class of image-ary image-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 image-ary image-cubes for odd integer image 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 image-ary image-cube image with odd image, every pair of healthy vertices of image are connected by fault-free paths of lengths from image to image and every healthy edge is contained in fault-free cycles of lengths from image to image for any set image of faulty elements (vertices and/or edges) with image. Finally, examples show that our results are best possible in some sense.