Minimal locating-paired-dominating sets in triangular and king grids
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....
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2018-08-01
|
| Series: | Kuwait Journal of Science |
| Subjects: | |
| Online Access: | https://journalskuwait.org/kjs/index.php/KJS/article/view/3897 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849434192649125888 |
|---|---|
| author | Mariam Kinawi Zaid Hussain Ludovit Niepel |
| author_facet | Mariam Kinawi Zaid Hussain Ludovit Niepel |
| author_sort | Mariam Kinawi |
| collection | DOAJ |
| description |
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
|
| format | Article |
| id | doaj-art-64e8dcb0f4fa4df5ade2ee46f460cdfe |
| institution | Kabale University |
| issn | 2307-4108 2307-4116 |
| language | English |
| publishDate | 2018-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Kuwait Journal of Science |
| spelling | doaj-art-64e8dcb0f4fa4df5ade2ee46f460cdfe2025-08-20T03:26:44ZengElsevierKuwait Journal of Science2307-41082307-41162018-08-01453Minimal locating-paired-dominating sets in triangular and king gridsMariam KinawiZaid Hussain0Ludovit NiepelComputer Sciece Kuwait University 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 https://journalskuwait.org/kjs/index.php/KJS/article/view/3897Locating-dominating setTriangular gridKing grid |
| spellingShingle | Mariam Kinawi Zaid Hussain Ludovit Niepel Minimal locating-paired-dominating sets in triangular and king grids Kuwait Journal of Science Locating-dominating set Triangular grid King grid |
| title | Minimal locating-paired-dominating sets in triangular and king grids |
| title_full | Minimal locating-paired-dominating sets in triangular and king grids |
| title_fullStr | Minimal locating-paired-dominating sets in triangular and king grids |
| title_full_unstemmed | Minimal locating-paired-dominating sets in triangular and king grids |
| title_short | Minimal locating-paired-dominating sets in triangular and king grids |
| title_sort | minimal locating paired dominating sets in triangular and king grids |
| topic | Locating-dominating set Triangular grid King grid |
| url | https://journalskuwait.org/kjs/index.php/KJS/article/view/3897 |
| work_keys_str_mv | AT mariamkinawi minimallocatingpaireddominatingsetsintriangularandkinggrids AT zaidhussain minimallocatingpaireddominatingsetsintriangularandkinggrids AT ludovitniepel minimallocatingpaireddominatingsetsintriangularandkinggrids |