image-labeling of direct product of paths and cycles Original Research Article

An image-labeling of a graph G is an assignment of labels from image to the vertices of G such that vertices at distance two get different labels and adjacent vertices get labels that are at least two apart. The image-number image of G is the minimum value image such that G admits an image-labeling. Let image denote the direct product of G and H. We compute the image-numbers for each of image, image, image, and image. We also show that for image and image, image if and only if image, image. The results are partially obtained by a computer search.