Total global neighbourhood domination
A subset D of the vertex set of a connected graph G is called a total global neighbourhood dominating set (tgnd-set) of G if and only if D is a total dominating set of G as well as GN, where GN is the neighbourhood graph of G. The total global neighbourhood domination number (tgnd-number) is the min...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/156643 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Total global neighbourhood domination / S.V. Siva Rama Raju, I.H. Nagaraja Rao // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 320-330. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862724505976176640 |
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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. |
| citation_txt | Total global neighbourhood domination / S.V. Siva Rama Raju, I.H. Nagaraja Rao // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 320-330. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | A subset D of the vertex set of a connected graph G is called a total global neighbourhood dominating set (tgnd-set) of G if and only if D is a total dominating set of G as well as GN, where GN is the neighbourhood graph of G. The total global neighbourhood domination number (tgnd-number) is the minimum cardinality of a total global neighbourhood dominating set of G and is denoted by γtgn(G). In this paper sharp bounds for γtgn 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(≥3) having tgnd-numbers 2,n−1,n.
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| first_indexed | 2025-12-07T18:48:10Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-156643 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:48:10Z |
| publishDate | 2017 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Siva Rama Raju, S.V. Nagaraja Rao, I.H. 2019-06-18T18:19:40Z 2019-06-18T18:19:40Z 2017 Total global neighbourhood domination / S.V. Siva Rama Raju, I.H. Nagaraja Rao // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 320-330. — Бібліогр.: 8 назв. — англ. 1726-3255 2010 MSC:05C69. https://nasplib.isofts.kiev.ua/handle/123456789/156643 A subset D of the vertex set of a connected graph G is called a total global neighbourhood dominating set (tgnd-set) of G if and only if D is a total dominating set of G as well as GN, where GN is the neighbourhood graph of G. The total global neighbourhood domination number (tgnd-number) is the minimum cardinality of a total global neighbourhood dominating set of G and is denoted by γtgn(G). In this paper sharp bounds for γtgn 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(≥3) having tgnd-numbers 2,n−1,n. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Total global neighbourhood domination Article published earlier |
| spellingShingle | Total global neighbourhood domination Siva Rama Raju, S.V. Nagaraja Rao, I.H. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156643 |
| work_keys_str_mv | AT sivaramarajusv totalglobalneighbourhooddomination AT nagarajaraoih totalglobalneighbourhooddomination |