A note on the weakly convex and convex domination numbers of a torus

The distance image between two vertices image and image in a connected graph image is the length of the shortest image path in image. A image path of length image is called a image-geodesic. A set image is called weakly convex in image if for every two vertices image, exists an image-geodesic, all of whose vertices belong to image. A set image is convex in image if for all image all vertices from every image-geodesic belong to image. The weakly convex domination number of a graph image is the minimum cardinality of a weakly convex dominating set of image, while the convex domination number of a graph image is the minimum cardinality of a convex dominating set of image. In this paper we consider weakly convex and convex domination numbers of tori.