Graphs with Total Domination Number Double of the Matching Number
A subset $S$ of vertices of a graph $G$ with no isolated vertex is called a total dominating set of $G$ if each vertex of $G$ has at least one neighbor in the set $S$. The total domination number $\gamma_t(G)$ of a graph $G$ is the minimum value of the size of a total dominating set of $G$. A subset...
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| Language: | English |
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Naim Çağman
2024-12-01
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| Series: | Journal of New Theory |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4089560 |
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| author | Selim Bahadır |
| author_facet | Selim Bahadır |
| author_sort | Selim Bahadır |
| collection | DOAJ |
| description | A subset $S$ of vertices of a graph $G$ with no isolated vertex is called a total dominating set of $G$ if each vertex of $G$ has at least one neighbor in the set $S$. The total domination number $\gamma_t(G)$ of a graph $G$ is the minimum value of the size of a total dominating set of $G$. A subset $M$ of the edges of a graph $G$ is called a matching if no two edges of $M$ have a common vertex. The matching number $\nu (G)$ of a graph $G$ is the maximum value of the size of a matching in $G$. It can be observed that $\gamma_t(G)\leq 2\nu(G)$ holds for every graph $G$ with no isolated vertex. This paper studies the graphs satisfying the equality and proves that $\gamma_t(G)= 2\nu(G)$ if and only if every connected component of $G$ is either a triangle or a star. |
| format | Article |
| id | doaj-art-a484344f6eee41b7b7f9f34f7e84a377 |
| institution | DOAJ |
| issn | 2149-1402 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Naim Çağman |
| record_format | Article |
| series | Journal of New Theory |
| spelling | doaj-art-a484344f6eee41b7b7f9f34f7e84a3772025-08-20T03:10:56ZengNaim ÇağmanJournal of New Theory2149-14022024-12-01491610.53570/jnt.15205572425Graphs with Total Domination Number Double of the Matching NumberSelim Bahadır0https://orcid.org/0000-0003-1533-7194ANKARA YILDIRIM BEYAZIT ÜNİVERSİTESİA subset $S$ of vertices of a graph $G$ with no isolated vertex is called a total dominating set of $G$ if each vertex of $G$ has at least one neighbor in the set $S$. The total domination number $\gamma_t(G)$ of a graph $G$ is the minimum value of the size of a total dominating set of $G$. A subset $M$ of the edges of a graph $G$ is called a matching if no two edges of $M$ have a common vertex. The matching number $\nu (G)$ of a graph $G$ is the maximum value of the size of a matching in $G$. It can be observed that $\gamma_t(G)\leq 2\nu(G)$ holds for every graph $G$ with no isolated vertex. This paper studies the graphs satisfying the equality and proves that $\gamma_t(G)= 2\nu(G)$ if and only if every connected component of $G$ is either a triangle or a star.https://dergipark.org.tr/en/download/article-file/4089560domination numbermatching numbertotal domination number |
| spellingShingle | Selim Bahadır Graphs with Total Domination Number Double of the Matching Number Journal of New Theory domination number matching number total domination number |
| title | Graphs with Total Domination Number Double of the Matching Number |
| title_full | Graphs with Total Domination Number Double of the Matching Number |
| title_fullStr | Graphs with Total Domination Number Double of the Matching Number |
| title_full_unstemmed | Graphs with Total Domination Number Double of the Matching Number |
| title_short | Graphs with Total Domination Number Double of the Matching Number |
| title_sort | graphs with total domination number double of the matching number |
| topic | domination number matching number total domination number |
| url | https://dergipark.org.tr/en/download/article-file/4089560 |
| work_keys_str_mv | AT selimbahadır graphswithtotaldominationnumberdoubleofthematchingnumber |