On unicyclic graphs of metric dimension 2 with vertices of degree 4
We show that if \(G\) is a unicyclic graph with metric dimension \(2\) and \(\{a,b\}\) is a metric basis of \(G\) then the degree of any vertex \(v\) of \(G\) is at most \(4\) and degrees of both \(a\) and \(b\) are at most \(2\). The constructions of unispider and semiunispider graphs and their k...
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| Datum: | 2019 |
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| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2019
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1265 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543027832553473 |
|---|---|
| author | Dudenko, Marharyta Oliynyk, Bogdana |
| author_facet | Dudenko, Marharyta Oliynyk, Bogdana |
| author_sort | Dudenko, Marharyta |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2019-01-24T08:21:31Z |
| description | We show that if \(G\) is a unicyclic graph with metric dimension \(2\) and \(\{a,b\}\) is a metric basis of \(G\) then the degree of any vertex \(v\) of \(G\) is at most \(4\) and degrees of both \(a\) and \(b\) are at most \(2\). The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constructions all unicyclic graphs of metric dimension \(2\) with vertices of degree \(4\) are characterized. |
| first_indexed | 2025-12-02T15:38:40Z |
| format | Article |
| id | admjournalluguniveduua-article-1265 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:38:40Z |
| publishDate | 2019 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-12652019-01-24T08:21:31Z On unicyclic graphs of metric dimension 2 with vertices of degree 4 Dudenko, Marharyta Oliynyk, Bogdana graph, distance, metric dimension, unicyclic graph 05C12 We show that if \(G\) is a unicyclic graph with metric dimension \(2\) and \(\{a,b\}\) is a metric basis of \(G\) then the degree of any vertex \(v\) of \(G\) is at most \(4\) and degrees of both \(a\) and \(b\) are at most \(2\). The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constructions all unicyclic graphs of metric dimension \(2\) with vertices of degree \(4\) are characterized. Lugansk National Taras Shevchenko University International Charitable Foundation for Renaissance of the Kyiv-Mohyla Academy 2019-01-24 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1265 Algebra and Discrete Mathematics; Vol 26, No 2 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1265/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1265/440 Copyright (c) 2019 Algebra and Discrete Mathematics |
| spellingShingle | graph distance metric dimension unicyclic graph 05C12 Dudenko, Marharyta Oliynyk, Bogdana On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title | On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title_full | On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title_fullStr | On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title_full_unstemmed | On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title_short | On unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| title_sort | on unicyclic graphs of metric dimension 2 with vertices of degree 4 |
| topic | graph distance metric dimension unicyclic graph 05C12 |
| topic_facet | graph distance metric dimension unicyclic graph 05C12 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1265 |
| work_keys_str_mv | AT dudenkomarharyta onunicyclicgraphsofmetricdimension2withverticesofdegree4 AT oliynykbogdana onunicyclicgraphsofmetricdimension2withverticesofdegree4 |