TY - JOUR
ID - 6390
TI - The arrow edge domination in graphs
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Abdlhusein, Mohammed A.
AU - Radhi, Suha J.
AD - College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq
Y1 - 2022
PY - 2022
VL - 13
IS - 2
SP - 591
EP - 597
KW - Arrow edge domination
KW - edge domination
KW - dominating set
KW - path graph
KW - cycle graph
DO - 10.22075/ijnaa.2022.6390
N2 - The 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.
UR - https://ijnaa.semnan.ac.ir/article_6390.html
L1 - https://ijnaa.semnan.ac.ir/article_6390_acc32f2872e3d0069a528ba04a1ba8f0.pdf
ER -