Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213220220701The arrow edge domination in graphs591597639010.22075/ijnaa.2022.6390ENMohammed A.AbdlhuseinCollege of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, IraqSuha J.RadhiCollege of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, IraqJournal Article20220102The idea of this paper is to study the arrow edge domination. The arrow edge dominating set $D_{e}$ of a graph $G$ is an arrow edge dominating set if every edge from $D$ dominates exactly one edge from $V-D$ and is adjacent to two or more edges from $D$. The arrow edge domination number $\gamma_{\text {are }}(G)$ is the minimum cardinality of all arrow edge dominating sets in $G$. Several properties and bounds are introduced here. Our results are applied in some graphs such that the path graph, cycle graph, complete graph, wheel graph, complete bipartite graph, Barbell graph, helm graph, big helm graph, complement path graph, complement cycle graph, the complement of complete graph and complement of complete bipartite graph. An important fact given here is if $G$ has no arrow vertex dominating set, then $G$ may have an arrow edge dominating set and an example is given.https://ijnaa.semnan.ac.ir/article_6390_acc32f2872e3d0069a528ba04a1ba8f0.pdf