Independent injective domination of graphs. (English) Zbl 1367.05152

Alwardi, Anwar; Alqesmah, Akram; Rangarajan, R.

Int. J. Adv. Appl. Math. Mech. 3, No. 4, 142-151 (2016).

Summary: An injective dominating set \(S\) in a graph \(G\) is called independent injective dominating set (IInj-dominating set) if for every \(v \in S\), \(N(v) \cap S = \phi\). The minimum cardinality of such injective dominating set is called independent injective domination number of \(G\) and denoted by \(\gamma_{iin}(G)\). In this paper, we introduce the independent injective domination of graphs and we define the IID-graph. Exact values for some families of graphs, relations with the other domination parameters are obtained. Also, we introduce the independent injective frustration number of graphs. Bounds and some interesting results are established.

MSC:

05C69

Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)

Keywords:

independent injective domination; injective domination; IID-graph; independent injective frustration number