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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| Date: | 2017 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2017
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.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| Summary: | 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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