Domination number on an octagonal chain and an octagonal grid
UDC 519.1 Domination of the graph and topological indices are essential topics in the graph theory. We analyze the problem of $k$-domination, $k\in\{1,2,3\}$, on octagonal chains and an octagonal grid. We determine the minimal $k$-dominating sets and&nb...
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7995 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512840070201344 |
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| author | Mihajlov Carević, Miroslava Mihajlov Carević, Miroslava |
| author_facet | Mihajlov Carević, Miroslava Mihajlov Carević, Miroslava |
| author_sort | Mihajlov Carević, Miroslava |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-08-28T14:54:53Z |
| description | UDC 519.1
Domination of the graph and topological indices are essential topics in the graph theory. We analyze the problem of $k$-domination, $k\in\{1,2,3\}$, on octagonal chains and an octagonal grid. We determine the minimal $k$-dominating sets and  $k$-domination $k$ numbers for a chain of octagons with two common vertices. By using the obtained results, we determine the $k$-domination numbers for the grid of octagons  $O_{mxn}$ with $m,n\in N$. |
| doi_str_mv | 10.3842/umzh.v76i12.7995 |
| first_indexed | 2026-03-24T03:35:10Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7995 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:35:10Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-79952025-08-28T14:54:53Z Domination number on an octagonal chain and an octagonal grid Domination number on an octagonal chain and an octagonal grid Mihajlov Carević, Miroslava Mihajlov Carević, Miroslava dominating set, domination number, chain of octagons, octagonal grid, coverage index. Dominance on the octagonal graph UDC 519.1 Domination of the graph and topological indices are essential topics in the graph theory. We analyze the problem of $k$-domination, $k\in\{1,2,3\}$, on octagonal chains and an octagonal grid. We determine the minimal $k$-dominating sets and  $k$-domination $k$ numbers for a chain of octagons with two common vertices. By using the obtained results, we determine the $k$-domination numbers for the grid of octagons  $O_{mxn}$ with $m,n\in N$. УДК 519.1 Число домінування на восьмикутному ланцюжку та восьмикутній сітці Домінування графа та топологічні індекси є важливими темами в теорії графів. Mи аналізуємо проблему $k$-домінування, $k\in\{1,2,3\}$, на восьмикутних ланцюгах і восьмикутній сітці. Визначено мінімальні $k$-домінуючі множини та $k$-домінування чисел для ланцюжка восьмикутників, що мають дві спільні вершини. Використовуючи отримані результати, ми визначаємо числа $k$-домінування для сітки восьмикутників $O_{mxn},$ де $m,n\in N$. Institute of Mathematics, NAS of Ukraine 2025-08-27 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7995 10.3842/umzh.v76i12.7995 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 12 (2024); 1738–1751 Український математичний журнал; Том 76 № 12 (2024); 1738–1751 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7995/10287 Copyright (c) 2024 Miroslava Mihajlov Carević |
| spellingShingle | Mihajlov Carević, Miroslava Mihajlov Carević, Miroslava Domination number on an octagonal chain and an octagonal grid |
| title | Domination number on an octagonal chain and an octagonal grid |
| title_alt | Domination number on an octagonal chain and an octagonal grid |
| title_full | Domination number on an octagonal chain and an octagonal grid |
| title_fullStr | Domination number on an octagonal chain and an octagonal grid |
| title_full_unstemmed | Domination number on an octagonal chain and an octagonal grid |
| title_short | Domination number on an octagonal chain and an octagonal grid |
| title_sort | domination number on an octagonal chain and an octagonal grid |
| topic_facet | dominating set domination number chain of octagons octagonal grid coverage index. Dominance on the octagonal graph |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7995 |
| work_keys_str_mv | AT mihajlovcarevicmiroslava dominationnumberonanoctagonalchainandanoctagonalgrid AT mihajlovcarevicmiroslava dominationnumberonanoctagonalchainandanoctagonalgrid |