Metric dimension of metric transform and wreath product
Let $(X,d)$ be a metric space. A non-empty subset $A$ of the set $X$ is called resolving set of the metric space $(X,d)$ if for two arbitrary not equal points $u,v$ from $X$ there exists an element $a$ from $A$, such that $d(u,a) \neq d(v,a)$. The smallest of cardinalities of resolving subsets of th...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2019-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/2119 |
| _version_ | 1818175354669367296 |
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| author | B.S. Ponomarchuk |
| author_facet | B.S. Ponomarchuk |
| author_sort | B.S. Ponomarchuk |
| collection | DOAJ |
| description | Let $(X,d)$ be a metric space. A non-empty subset $A$ of the set $X$ is called resolving set of the metric space $(X,d)$ if for two arbitrary not equal points $u,v$ from $X$ there exists an element $a$ from $A$, such that $d(u,a) \neq d(v,a)$. The smallest of cardinalities of resolving subsets of the set $X$ is called the metric dimension $md(X)$ of the metric space $(X,d)$.
In general, finding the metric dimension is an NP-hard problem. In this paper, metric dimension for metric transform and wreath product of metric spaces are provided. It is shown that the metric dimension of an arbitrary metric space is equal to the metric dimension of its metric transform. |
| first_indexed | 2024-12-11T19:58:58Z |
| format | Article |
| id | doaj.art-8346a7c35fb04934b126d020fd5b6fcf |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-12-11T19:58:58Z |
| publishDate | 2019-12-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-8346a7c35fb04934b126d020fd5b6fcf2022-12-22T00:52:34ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102019-12-0111241842110.15330/cmp.11.2.418-4212119Metric dimension of metric transform and wreath productB.S. Ponomarchuk0National University of Kyiv-Mohyla Academy, 2 Skovorody str., 04070, Kyiv, UkraineLet $(X,d)$ be a metric space. A non-empty subset $A$ of the set $X$ is called resolving set of the metric space $(X,d)$ if for two arbitrary not equal points $u,v$ from $X$ there exists an element $a$ from $A$, such that $d(u,a) \neq d(v,a)$. The smallest of cardinalities of resolving subsets of the set $X$ is called the metric dimension $md(X)$ of the metric space $(X,d)$. In general, finding the metric dimension is an NP-hard problem. In this paper, metric dimension for metric transform and wreath product of metric spaces are provided. It is shown that the metric dimension of an arbitrary metric space is equal to the metric dimension of its metric transform.https://journals.pnu.edu.ua/index.php/cmp/article/view/2119metric dimensionmetric transformwreath product |
| spellingShingle | B.S. Ponomarchuk Metric dimension of metric transform and wreath product Karpatsʹkì Matematičnì Publìkacìï metric dimension metric transform wreath product |
| title | Metric dimension of metric transform and wreath product |
| title_full | Metric dimension of metric transform and wreath product |
| title_fullStr | Metric dimension of metric transform and wreath product |
| title_full_unstemmed | Metric dimension of metric transform and wreath product |
| title_short | Metric dimension of metric transform and wreath product |
| title_sort | metric dimension of metric transform and wreath product |
| topic | metric dimension metric transform wreath product |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/2119 |
| work_keys_str_mv | AT bsponomarchuk metricdimensionofmetrictransformandwreathproduct |