A note on the weakly convex and convex domination numbers of a torus |
| |
Authors: | Joanna Raczek Magdalena Lemańska |
| |
Institution: | Department of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland |
| |
Abstract: | The distancedG(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 dG(u,v) is called a (u,v)-geodesic. A set X⊆V is called weakly convex in G if for every two vertices a,b∈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∈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. |
| |
Keywords: | Domination number Convex sets Torus |
本文献已被 ScienceDirect 等数据库收录! |
|