Global outer connected domination number of a graph
For a given graph \(G=(V,E)\), a dominating set \(D \subseteq V(G)\) is said to be an outer connected dominating set if \(D=V(G)\) or \(G-D\) is connected. The outer connected domination number of a graph \(G\), denoted by \(\widetilde{\gamma}_c(G)\), is the cardinality of a minimum outer connected...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/126 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-1262018-05-17T07:54:05Z Global outer connected domination number of a graph Alishahi, Morteza Mojdeh, Doost Ali global domination, outer connected domination, global outer connected domination, trees 05C69 For a given graph \(G=(V,E)\), a dominating set \(D \subseteq V(G)\) is said to be an outer connected dominating set if \(D=V(G)\) or \(G-D\) is connected. The outer connected domination number of a graph \(G\), denoted by \(\widetilde{\gamma}_c(G)\), is the cardinality of a minimum outer connected dominating set of \(G\). A set \(S \subseteq V(G)\) is said to be a global outer connected dominating set of a graph \(G\) if \(S\) is an outer connected dominating set of \(G\) and \(\overline G\). The global outer connected domination number of a graph \(G\), denoted by \(\widetilde{\gamma}_{gc}(G)\), is the cardinality of a minimum global outer connected dominating set of \(G\). In this paper we obtain some bounds for outer connected domination numbers and global outer connected domination numbers of graphs. In particular, we show that for connected graph \(G\ne K_1\), \( \max\{{n-\frac{m+1}{2}}, \frac{5n+2m-n^2-2}{4}\} \leq \widetilde{\gamma}_{gc}(G) \leq \min\{m(G),m(\overline G)\}\). Finally, under the conditions, we show the equality of global outer connected domination numbers and outer connected domination numbers for family of trees. Lugansk National Taras Shevchenko University 2018-04-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/126 Algebra and Discrete Mathematics; Vol 25, No 1 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/126/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/126/314 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
global domination outer connected domination global outer connected domination trees 05C69 |
| spellingShingle |
global domination outer connected domination global outer connected domination trees 05C69 Alishahi, Morteza Mojdeh, Doost Ali Global outer connected domination number of a graph |
| topic_facet |
global domination outer connected domination global outer connected domination trees 05C69 |
| format |
Article |
| author |
Alishahi, Morteza Mojdeh, Doost Ali |
| author_facet |
Alishahi, Morteza Mojdeh, Doost Ali |
| author_sort |
Alishahi, Morteza |
| title |
Global outer connected domination number of a graph |
| title_short |
Global outer connected domination number of a graph |
| title_full |
Global outer connected domination number of a graph |
| title_fullStr |
Global outer connected domination number of a graph |
| title_full_unstemmed |
Global outer connected domination number of a graph |
| title_sort |
global outer connected domination number of a graph |
| description |
For a given graph \(G=(V,E)\), a dominating set \(D \subseteq V(G)\) is said to be an outer connected dominating set if \(D=V(G)\) or \(G-D\) is connected. The outer connected domination number of a graph \(G\), denoted by \(\widetilde{\gamma}_c(G)\), is the cardinality of a minimum outer connected dominating set of \(G\). A set \(S \subseteq V(G)\) is said to be a global outer connected dominating set of a graph \(G\) if \(S\) is an outer connected dominating set of \(G\) and \(\overline G\). The global outer connected domination number of a graph \(G\), denoted by \(\widetilde{\gamma}_{gc}(G)\), is the cardinality of a minimum global outer connected dominating set of \(G\). In this paper we obtain some bounds for outer connected domination numbers and global outer connected domination numbers of graphs. In particular, we show that for connected graph \(G\ne K_1\), \( \max\{{n-\frac{m+1}{2}}, \frac{5n+2m-n^2-2}{4}\} \leq \widetilde{\gamma}_{gc}(G) \leq \min\{m(G),m(\overline G)\}\). Finally, under the conditions, we show the equality of global outer connected domination numbers and outer connected domination numbers for family of trees. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/126 |
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AT alishahimorteza globalouterconnecteddominationnumberofagraph AT mojdehdoostali globalouterconnecteddominationnumberofagraph |
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2024-04-12T06:26:02Z |
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2024-04-12T06:26:02Z |
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