TY - JOUR
ID - 4826
TI - The arrow domination in graphs
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Radhi, Suha Jaber
AU - A. Abdlhusein, Mohammed
AU - Hashoosh, Ayed Elayose
AD - Department of Mathematics, College of Education for Pure Sciences,
University of Thi-Qar, Thi-Qar, Iraq
AD - Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq
Y1 - 2021
PY - 2021
VL - 12
IS - 1
SP - 473
EP - 480
KW - Dominating set
KW - Arrow dominating set
KW - Arrow domination number
DO - 10.22075/ijnaa.2021.4826
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_4826.html
L1 - https://ijnaa.semnan.ac.ir/article_4826_feb89c6dfd48529e1560f0505d4fe521.pdf
ER -