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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Naim Çağman
2024-12-01
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| Series: | Journal of New Theory |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/4089560 |
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| Summary: | 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. |
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| ISSN: | 2149-1402 |