The 2-distance coloring of the Cartesian product of cycles using optimal Lee codes Original Research Article

Let image be the cycle of length image. We denote the Cartesian product of image copies of image by image. The image-distance chromatic number image of a graph image is image where image is the imageth power of the graph image in which two distinct vertices are adjacent in image if and only if their distance in image is at most image. The image-distance chromatic number of image is related to optimal codes over the ring of integers modulo image with minimum Lee distance image. In this paper, we consider image for image and image. In particular, we compute exact values of image for image and image, and upper bounds for image or image, for any positive integer image. We also show that the maximal size of a code in image with minimum Lee distance 3 is 26.