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Algebra and Discrete Mathematics, 2017, том 24, выпуск 2, страницы 320–330
(Mi adm637)
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RESEARCH ARTICLE
Total global neighbourhood domination
S. V. Siva Rama Rajuab, I. H. Nagaraja Raoc a Academic Support Department, Abu Dhabi Polytechnic, Al Ain, United Arab Emirates
b Department of Information Technology, Ibra college of Technology,
Ibra, Sultanate of Oman
c Laxmikantham Institute of Advanced Studies, G.V.P. College of Engineering, Visakhapatnam, India
Аннотация:
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 $2, n - 1, n$.
Ключевые слова:
semi complete graph, total dominating set, connected dominating set.
Поступила в редакцию: 19.10.2015 Исправленный вариант: 06.11.2015
Образец цитирования:
S. V. Siva Rama Raju, I. H. Nagaraja Rao, “Total global neighbourhood domination”, Algebra Discrete Math., 24:2 (2017), 320–330
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm637 https://www.mathnet.ru/rus/adm/v24/i2/p320
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