@article {
author = {Radhi, Suha and A. Abdlhusein, Mohammed and Hashoosh, Ayed},
title = {The arrow domination in graphs},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {12},
number = {1},
pages = {473-480},
year = {2021},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2021.4826},
abstract = {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.},
keywords = {Dominating set,Arrow dominating set,Arrow domination number},
url = {https://ijnaa.semnan.ac.ir/article_4826.html},
eprint = {https://ijnaa.semnan.ac.ir/article_4826_feb89c6dfd48529e1560f0505d4fe521.pdf}
}