Some results on the open locating-total domination number in graphs
In this paper, we generalize the concept of an open locating-dominating set in graphs. We introduce a concept as an open locating-total dominating set in graphs that is equivalent to the open neighborhood locating-dominating set. A vertex set $S \subseteq V(G)$ is an open locating-total dominating i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2023-01-01
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| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_3325_79f9b969ef43bf7e7129c1d93494c7b4.pdf |
| Summary: | In this paper, we generalize the concept of an open locating-dominating set in graphs. We introduce a concept as an open locating-total dominating set in graphs that is equivalent to the open neighborhood locating-dominating set. A vertex set $S \subseteq V(G)$ is an open locating-total dominating if the set $S$ is a total dominating set of $G$ and for any pair of distinct vertices $x$ and $y$ in $V(G)$, $N(x) \cap S\neq N(y) \cap S$. The open locating-total domination number, denoted $\gamma_{t}^{OL}(G)$, of $G$ is the minimum cardinality of an open locating-total dominating set. In this paper, we determine the open locating-total dominating set of some families of graphs. Also, the open locating-total domination number is calculated for two families of trees. The present paper is an extended version of our paper, presented at the 52nd Annual Iranian Mathematics Conference, Shahid Bahonar University of Kerman, Iran, 2021. |
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| ISSN: | 2251-7952 2645-4505 |