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The arrow domination in graphs | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 36، دوره 12، شماره 1، مرداد 2021، صفحه 473-480 اصل مقاله (359.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4826 | ||
| نویسندگان | ||
| Suha Jaber Radhi1؛ Mohammed A. Abdlhusein* 2؛ Ayed Elayose Hashoosh1 | ||
| 1Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq | ||
| 2Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq | ||
| تاریخ دریافت: 20 آذر 1399، تاریخ بازنگری: 24 دی 1399، تاریخ پذیرش: 16 بهمن 1399 | ||
| چکیده | ||
| The arrow domination is introduced in this paper with its inverse as a new type of domination. Let $G$ be a finite graph, undirected, simple and has no isolated vertex, a set $D$ of $V(G)$ is said an arrow dominating set if $|N(w)\cap (V-D)|=i$ and $|N(w)\cap D|\geq j$ for every $w \in D$ such that $i$ and $j$ are two non-equal positive integers. The arrow domination number $\gamma_{ar}(G)$ is the minimum cardinality over all arrow dominating sets in $G$. Essential properties and bounds of arrow domination and its inverse when $i=1$ and $j=2$ are proved. Then, arrow domination number is discussed for several standard graphs and other graphs that formed by join and corona operations. | ||
| کلیدواژه‌ها | ||
| Dominating set؛ Arrow dominating set؛ Arrow domination number | ||
| مراجع | ||
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