Bounds on weak and strong total domination in graphs
A set $D$ of vertices in a graph $G=(V,E)$ is a total dominating<br />set if every vertex of $G$ is adjacent to some vertex in $D$. A<br />total dominating set $D$ of $G$ is said to be weak if every<br />vertex $v\in V-D$ is adjacent to a vertex $u\in D$ such that<br />$d_{G}...
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| Format: | Article |
| Language: | English |
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Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
2016-04-01
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| Series: | Electronic Journal of Graph Theory and Applications |
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| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/141 |
| _version_ | 1828218548838727680 |
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| author | M.H. Akhbari Nader Jafari Rad |
| author_facet | M.H. Akhbari Nader Jafari Rad |
| author_sort | M.H. Akhbari |
| collection | DOAJ |
| description | A set $D$ of vertices in a graph $G=(V,E)$ is a total dominating<br />set if every vertex of $G$ is adjacent to some vertex in $D$. A<br />total dominating set $D$ of $G$ is said to be weak if every<br />vertex $v\in V-D$ is adjacent to a vertex $u\in D$ such that<br />$d_{G}(v)\geq d_{G}(u)$. The weak total domination number<br />$\gamma_{wt}(G)$ of $G$ is the minimum cardinality of a weak<br />total dominating set of $G$. A total dominating set $D$ of $G$ is<br />said to be strong if every vertex $v\in V-D$ is adjacent to a<br />vertex $u\in D$ such that $d_{G}(v)\leq d_{G}(u)$. The strong<br />total domination number $\gamma_{st}(G)$ of $G$ is the minimum<br />cardinality of a strong total dominating set of $G$. We present<br />some bounds on weak and strong total domination number of a graph. |
| first_indexed | 2024-04-12T16:04:33Z |
| format | Article |
| id | doaj.art-87825bca134746f9886762522be9b555 |
| institution | Directory Open Access Journal |
| issn | 2338-2287 |
| language | English |
| last_indexed | 2024-04-12T16:04:33Z |
| publishDate | 2016-04-01 |
| publisher | Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia |
| record_format | Article |
| series | Electronic Journal of Graph Theory and Applications |
| spelling | doaj.art-87825bca134746f9886762522be9b5552022-12-22T03:26:06ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872016-04-014111111810.5614/ejgta.2016.4.1.1061Bounds on weak and strong total domination in graphsM.H. Akhbari0Nader Jafari Rad1Department of Mathematics, Estahban Branch, Islamic Azad University, Estahban, IranDepartment of Mathematics, Shahrood University of Technology, Shahrood, IranA set $D$ of vertices in a graph $G=(V,E)$ is a total dominating<br />set if every vertex of $G$ is adjacent to some vertex in $D$. A<br />total dominating set $D$ of $G$ is said to be weak if every<br />vertex $v\in V-D$ is adjacent to a vertex $u\in D$ such that<br />$d_{G}(v)\geq d_{G}(u)$. The weak total domination number<br />$\gamma_{wt}(G)$ of $G$ is the minimum cardinality of a weak<br />total dominating set of $G$. A total dominating set $D$ of $G$ is<br />said to be strong if every vertex $v\in V-D$ is adjacent to a<br />vertex $u\in D$ such that $d_{G}(v)\leq d_{G}(u)$. The strong<br />total domination number $\gamma_{st}(G)$ of $G$ is the minimum<br />cardinality of a strong total dominating set of $G$. We present<br />some bounds on weak and strong total domination number of a graph.https://www.ejgta.org/index.php/ejgta/article/view/141weak total domination, strong total domination, nordhaus-gaddum |
| spellingShingle | M.H. Akhbari Nader Jafari Rad Bounds on weak and strong total domination in graphs Electronic Journal of Graph Theory and Applications weak total domination, strong total domination, nordhaus-gaddum |
| title | Bounds on weak and strong total domination in graphs |
| title_full | Bounds on weak and strong total domination in graphs |
| title_fullStr | Bounds on weak and strong total domination in graphs |
| title_full_unstemmed | Bounds on weak and strong total domination in graphs |
| title_short | Bounds on weak and strong total domination in graphs |
| title_sort | bounds on weak and strong total domination in graphs |
| topic | weak total domination, strong total domination, nordhaus-gaddum |
| url | https://www.ejgta.org/index.php/ejgta/article/view/141 |
| work_keys_str_mv | AT mhakhbari boundsonweakandstrongtotaldominationingraphs AT naderjafarirad boundsonweakandstrongtotaldominationingraphs |