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An inverse triple effect domination in graphs | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 913-919 اصل مقاله (394.44 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5147 | ||
| نویسندگان | ||
| Zinah H. Abdulhasan؛ Mohammed A. Abdlhusein* | ||
| Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq | ||
| تاریخ دریافت: 18 بهمن 1399، تاریخ بازنگری: 06 فروردین 1400، تاریخ پذیرش: 14 فروردین 1400 | ||
| چکیده | ||
| In this paper, an inverse triple effect domination is introduced for any finite graph $G=(V, E)$ simple and undirected without isolated vertices. A subset $D^{-1}$ of $V-D$ is an inverse triple effect dominating set if every $v \in D^{-1}$ dominates exactly three vertices of $V-D^{-1}$. The inverse triple effect domination number $\gamma_{t e}^{-1}(G)$ is the minimum cardinality over all inverse triple effect dominating sets in $G$. Some results and properties on $\gamma_{t e}^{-1}(G)$ are given and proved. Under any conditions the graph satisfies $\gamma_{t e}(G)+\gamma_{t e}^{-1}(G)=n$ is studied. Lower and upper bounds for the size of a graph that has $\gamma_{t e}^{-1}(G)$ are putted in two cases when $D^{-1}=V-D$ and when $D^{-1} \neq V-D .$ Which properties of a vertex to be belongs to $D^{-1}$ or out of it are discussed. Then, $\gamma_{t e}^{-1}(G)$ is evaluated and proved for several graphs. | ||
| کلیدواژه‌ها | ||
| Dominating set؛ Triple effect domination؛ Inverse triple effect domination | ||
| مراجع | ||
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