Title of article :
The arrow domination in graphs
Author/Authors :
Radhi, Suha J. Department of Mathematics - College of Education for Pure Sciences - University of Thi-Qar, Thi-Qar, Iraq , Abdlhusein, Mohammed A. Department of Mathematics - College of Education for Pure Sciences - University of Thi-Qar, Thi-Qar, Iraq , Hashoosha, Ayed E. Department of Mathematics - College of Education for Pure Sciences - University of Thi-Qar, Thi-Qar, Iraq
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)∩(V−D)|=i and |N(w)∩D|≥j for every w∈D such that i and j are two non-equal positive integers. The arrow domination number γar(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
Journal title :
International Journal of Nonlinear Analysis and Applications
