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

作者：Raczek Joanna^*; Lemanska Magdalena

来源：Discrete Applied Mathematics, 2010, 158(15): 1708-1713.

DOI：10.1016/j.dam.2010.06.001

• Domination number
• Convex sets
• Torus

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

• 出版日期2010-8-6