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: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2023-01-01
|
| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_3325_79f9b969ef43bf7e7129c1d93494c7b4.pdf |
| _version_ | 1797799221987901440 |
|---|---|
| author | Fateme Movahedi Mohammad Hadi Akhbari |
| author_facet | Fateme Movahedi Mohammad Hadi Akhbari |
| author_sort | Fateme Movahedi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-13T04:16:43Z |
| format | Article |
| id | doaj.art-741ef10f0a9d45589f85c94ec08b0bd1 |
| institution | Directory Open Access Journal |
| issn | 2251-7952 2645-4505 |
| language | English |
| last_indexed | 2024-03-13T04:16:43Z |
| publishDate | 2023-01-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj.art-741ef10f0a9d45589f85c94ec08b0bd12023-06-21T03:21:03ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052023-01-01121435810.22103/jmmr.2022.18693.11833325Some results on the open locating-total domination number in graphsFateme Movahedi0Mohammad Hadi Akhbari1Department of Mathematics, Golestan University, Gorgan, IranDepartment of Mathematics, Estahban Branch, Islamic Azad University Estahban, IranIn 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.https://jmmrc.uk.ac.ir/article_3325_79f9b969ef43bf7e7129c1d93494c7b4.pdfopen locating dominatingtotal dominating setcartesian product of graphs |
| spellingShingle | Fateme Movahedi Mohammad Hadi Akhbari Some results on the open locating-total domination number in graphs Journal of Mahani Mathematical Research open locating dominating total dominating set cartesian product of graphs |
| title | Some results on the open locating-total domination number in graphs |
| title_full | Some results on the open locating-total domination number in graphs |
| title_fullStr | Some results on the open locating-total domination number in graphs |
| title_full_unstemmed | Some results on the open locating-total domination number in graphs |
| title_short | Some results on the open locating-total domination number in graphs |
| title_sort | some results on the open locating total domination number in graphs |
| topic | open locating dominating total dominating set cartesian product of graphs |
| url | https://jmmrc.uk.ac.ir/article_3325_79f9b969ef43bf7e7129c1d93494c7b4.pdf |
| work_keys_str_mv | AT fatememovahedi someresultsontheopenlocatingtotaldominationnumberingraphs AT mohammadhadiakhbari someresultsontheopenlocatingtotaldominationnumberingraphs |