Minimal locating-paired-dominating sets in triangular and king grids

Kuwait Journal of Science

Mariam Kinawi¹ 

[1] Computer ScieceKuwait University

关键词: Locating-dominating set;    Triangular grid;    King grid;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: Kuwait University * Academic Publication Council

【 摘 要 】

Let G = (V,E) be a finite or infinite graph. A set S ? V is paired-dominating if S induces a matching in G and S dominates all vertices of G. A set S ? V is locating if for any two distinct vertices u, v in V \ S, N(u) ? S 6= N(v) ? S, where N(u) and N(v) are open neighborhoods of vertices u and v. We find the minimal density of locating-paired-dominating sets in the infinite triangular grid, which is equal to 4/15. We also present bounds for the minimal density D of locating-paired-dominating sets in the infinite king grid, which is 3/14 ? D ? 2/9

【 授权许可】

Unknown