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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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/86 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543043663953920 |
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| 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. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T02:43:18Z |
| 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 \(2, n - 1, n\). |
| first_indexed | 2025-12-02T15:41:11Z |
| format | Article |
| id | admjournalluguniveduua-article-86 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:41:11Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | semi complete graph total dominating set connected dominating set 05C69 Siva Rama Raju, S. V. Nagaraja Rao, I. H. Total global neighbourhood domination |
| title | Total global neighbourhood domination |
| title_full | Total global neighbourhood domination |
| title_fullStr | Total global neighbourhood domination |
| title_full_unstemmed | Total global neighbourhood domination |
| title_short | Total global neighbourhood domination |
| title_sort | total global neighbourhood domination |
| topic | semi complete graph total dominating set connected dominating set 05C69 |
| topic_facet | semi complete graph total dominating set connected dominating set 05C69 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/86 |
| work_keys_str_mv | AT sivaramarajusv totalglobalneighbourhooddomination AT nagarajaraoih totalglobalneighbourhooddomination |