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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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2017
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156643 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-156643 |
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irk-123456789-1566432019-06-19T01:27:51Z Total global neighbourhood domination Siva Rama Raju, S.V. Nagaraja Rao, I.H. 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. 2017 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/156643 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Siva Rama Raju, S.V. Nagaraja Rao, I.H. |
| spellingShingle |
Siva Rama Raju, S.V. Nagaraja Rao, I.H. Total global neighbourhood domination Algebra and Discrete Mathematics |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156643 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT sivaramarajusv totalglobalneighbourhooddomination AT nagarajaraoih totalglobalneighbourhooddomination |
| first_indexed |
2023-05-20T17:50:09Z |
| last_indexed |
2023-05-20T17:50:09Z |
| _version_ |
1796154203154939904 |