The arrow domination in graphs

‎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=۱ and j=۲ are proved‎. ‎Then‎, ‎arrow domination number is discussed for several standard graphs and other graphs that formed by join and corona operations‎.

کلیدواژه ها:

‎Dominating set‎ ، ‎Arrow dominating set‎ ، ‎Arrow domination number‎