A remark on the metric dimension in Riemannian manifolds of constant curvature
We compute the metric dimension of Riemannian manifolds of constant curvature. We define the edge weghited metric dimension of the geodesic graphs in Riemannian manifolds and we show that each complete geodesic graph $G=(V,E)$ embedded in a Riemannian manifold of constant curvature resolves a totall...
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| Format: | Article |
| Language: | English |
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Amirkabir University of Technology
2025-02-01
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| Series: | AUT Journal of Mathematics and Computing |
| Subjects: | |
| Online Access: | https://ajmc.aut.ac.ir/article_5326_701c1c6aa05ef2d0eabf0555883c95ae.pdf |
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| _version_ | 1823858248815476736 |
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| author | Shiva Heidarkhani Gilani Reza Mirzaie Ebrahim Vatandoost |
| author_facet | Shiva Heidarkhani Gilani Reza Mirzaie Ebrahim Vatandoost |
| author_sort | Shiva Heidarkhani Gilani |
| collection | DOAJ |
| description | We compute the metric dimension of Riemannian manifolds of constant curvature. We define the edge weghited metric dimension of the geodesic graphs in Riemannian manifolds and we show that each complete geodesic graph $G=(V,E)$ embedded in a Riemannian manifold of constant curvature resolves a totally geodesic submanifold of dimension $|V|-1$. |
| format | Article |
| id | doaj-art-2661298d7c6b485c8a5dae19478b98f0 |
| institution | Kabale University |
| issn | 2783-2449 2783-2287 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Amirkabir University of Technology |
| record_format | Article |
| series | AUT Journal of Mathematics and Computing |
| spelling | doaj-art-2661298d7c6b485c8a5dae19478b98f02025-02-11T12:37:04ZengAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24492783-22872025-02-016217117610.22060/ajmc.2023.22527.11655326A remark on the metric dimension in Riemannian manifolds of constant curvatureShiva Heidarkhani Gilani0Reza Mirzaie1Ebrahim Vatandoost2Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranWe compute the metric dimension of Riemannian manifolds of constant curvature. We define the edge weghited metric dimension of the geodesic graphs in Riemannian manifolds and we show that each complete geodesic graph $G=(V,E)$ embedded in a Riemannian manifold of constant curvature resolves a totally geodesic submanifold of dimension $|V|-1$.https://ajmc.aut.ac.ir/article_5326_701c1c6aa05ef2d0eabf0555883c95ae.pdfmetric dimensionriemannian manifoldgraph |
| spellingShingle | Shiva Heidarkhani Gilani Reza Mirzaie Ebrahim Vatandoost A remark on the metric dimension in Riemannian manifolds of constant curvature AUT Journal of Mathematics and Computing metric dimension riemannian manifold graph |
| title | A remark on the metric dimension in Riemannian manifolds of constant curvature |
| title_full | A remark on the metric dimension in Riemannian manifolds of constant curvature |
| title_fullStr | A remark on the metric dimension in Riemannian manifolds of constant curvature |
| title_full_unstemmed | A remark on the metric dimension in Riemannian manifolds of constant curvature |
| title_short | A remark on the metric dimension in Riemannian manifolds of constant curvature |
| title_sort | remark on the metric dimension in riemannian manifolds of constant curvature |
| topic | metric dimension riemannian manifold graph |
| url | https://ajmc.aut.ac.ir/article_5326_701c1c6aa05ef2d0eabf0555883c95ae.pdf |
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