Total global neighbourhood domination
A subset \(D\) of the vertex set of a connected graph \(G\) is called a total global neighbourhood dominating set (\(\mathrm{tgnd}\)-set) of \(G\) if and only if \(D\) is a total dominating set of \(G\) as well as \(G^{N}\), where \(G^{N}\) is the neighbourhood graph of \(G\). The total global neigh...
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| Дата: | 2018 |
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| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-862018-04-26T02:43:18Z Total global neighbourhood domination Siva Rama Raju, S. V. Nagaraja Rao, I. H. semi complete graph, total dominating set, connected dominating set 05C69 A subset \(D\) of the vertex set of a connected graph \(G\) is called a total global neighbourhood dominating set (\(\mathrm{tgnd}\)-set) of \(G\) if and only if \(D\) is a total dominating set of \(G\) as well as \(G^{N}\), where \(G^{N}\) is the neighbourhood graph of \(G\). The total global neighbourhood domination number (\(\mathrm{tgnd}\)-number) is the minimum cardinality of a total global neighbourhood dominating set of \(G\) and is denoted by \(\gamma_{\mathrm{tgn}}(G)\). In this paper sharp bounds for \(\gamma_{\mathrm{tgn}}\) are obtained. Exact values of this number for paths and cycles are presented as well. The characterization result for a subset of the vertex set of \(G\) to be a total global neighbourhood dominating set for \(G\) is given and also characterized the graphs of order \(n(\geq 3)\) having \(\mathrm{tgnd}\)-numbers \(2, n - 1, n\). Lugansk National Taras Shevchenko University 2018-01-24 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/86 Algebra and Discrete Mathematics; Vol 24, No 2 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/86/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/86/77 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
semi complete graph total dominating set connected dominating set 05C69 |
| spellingShingle |
semi complete graph total dominating set connected dominating set 05C69 Siva Rama Raju, S. V. Nagaraja Rao, I. H. Total global neighbourhood domination |
| topic_facet |
semi complete graph total dominating set connected dominating set 05C69 |
| format |
Article |
| author |
Siva Rama Raju, S. V. Nagaraja Rao, I. H. |
| author_facet |
Siva Rama Raju, S. V. Nagaraja Rao, I. H. |
| author_sort |
Siva Rama Raju, S. V. |
| title |
Total global neighbourhood domination |
| title_short |
Total global neighbourhood domination |
| title_full |
Total global neighbourhood domination |
| title_fullStr |
Total global neighbourhood domination |
| title_full_unstemmed |
Total global neighbourhood domination |
| title_sort |
total global neighbourhood domination |
| description |
A subset \(D\) of the vertex set of a connected graph \(G\) is called a total global neighbourhood dominating set (\(\mathrm{tgnd}\)-set) of \(G\) if and only if \(D\) is a total dominating set of \(G\) as well as \(G^{N}\), where \(G^{N}\) is the neighbourhood graph of \(G\). The total global neighbourhood domination number (\(\mathrm{tgnd}\)-number) is the minimum cardinality of a total global neighbourhood dominating set of \(G\) and is denoted by \(\gamma_{\mathrm{tgn}}(G)\). In this paper sharp bounds for \(\gamma_{\mathrm{tgn}}\) are obtained. Exact values of this number for paths and cycles are presented as well. The characterization result for a subset of the vertex set of \(G\) to be a total global neighbourhood dominating set for \(G\) is given and also characterized the graphs of order \(n(\geq 3)\) having \(\mathrm{tgnd}\)-numbers \(2, n - 1, n\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/86 |
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AT sivaramarajusv totalglobalneighbourhooddomination AT nagarajaraoih totalglobalneighbourhooddomination |
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2024-04-12T06:25:53Z |
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2024-04-12T06:25:53Z |
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