On unicyclic graphs of metric dimension \(2\)
A metric basis \(S\) of a graph \(G\) is the subset of vertices of minimum cardinality such that all other vertices are uniquely determined by their distances to the vertices in \(S\). The metric dimension of a graph \(G\) is the cardinality of the subset \(S\). A unicyclic graph is a graph con...
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2017
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/475 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543154217418752 |
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| author | Dudenko, Margaryta Oliynyk, Bogdana |
| author_facet | Dudenko, Margaryta Oliynyk, Bogdana |
| author_sort | Dudenko, Margaryta |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2017-07-02T21:58:40Z |
| description | A metric basis \(S\) of a graph \(G\) is the subset of vertices of minimum cardinality such that all other vertices are uniquely determined by their distances to the vertices in \(S\). The metric dimension of a graph \(G\) is the cardinality of the subset \(S\). A unicyclic graph is a graph containing exactly one cycle. The construction of a knitting unicyclic graph is introduced. Using this construction all unicyclic graphs with two main vertices and metric dimensions \(2\) are characterized. |
| first_indexed | 2026-02-08T07:58:43Z |
| format | Article |
| id | admjournalluguniveduua-article-475 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:43Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-4752017-07-02T21:58:40Z On unicyclic graphs of metric dimension \(2\) Dudenko, Margaryta Oliynyk, Bogdana distance, metric dimensions, unicyclic graph 05C12 A metric basis \(S\) of a graph \(G\) is the subset of vertices of minimum cardinality such that all other vertices are uniquely determined by their distances to the vertices in \(S\). The metric dimension of a graph \(G\) is the cardinality of the subset \(S\). A unicyclic graph is a graph containing exactly one cycle. The construction of a knitting unicyclic graph is introduced. Using this construction all unicyclic graphs with two main vertices and metric dimensions \(2\) are characterized. Lugansk National Taras Shevchenko University 2017-07-03 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/475 Algebra and Discrete Mathematics; Vol 23, No 2 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/475/pdf Copyright (c) 2017 Algebra and Discrete Mathematics |
| spellingShingle | distance metric dimensions unicyclic graph 05C12 Dudenko, Margaryta Oliynyk, Bogdana On unicyclic graphs of metric dimension \(2\) |
| title | On unicyclic graphs of metric dimension \(2\) |
| title_full | On unicyclic graphs of metric dimension \(2\) |
| title_fullStr | On unicyclic graphs of metric dimension \(2\) |
| title_full_unstemmed | On unicyclic graphs of metric dimension \(2\) |
| title_short | On unicyclic graphs of metric dimension \(2\) |
| title_sort | on unicyclic graphs of metric dimension \(2\) |
| topic | distance metric dimensions unicyclic graph 05C12 |
| topic_facet | distance metric dimensions unicyclic graph 05C12 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/475 |
| work_keys_str_mv | AT dudenkomargaryta onunicyclicgraphsofmetricdimension2 AT oliynykbogdana onunicyclicgraphsofmetricdimension2 |