On proper (1,2)‐dominating sets in graphs
Adrian Michalski, Iwona Włoch, Magda Dettlaff, Magdalena Lemańska · Mathematical Methods in the Applied Sciences · 2022
In 2008, Hedetniemi et al. introduced the concept of ‐domination and obtained some interesting results for ‐domination. Obviously every ‐dominating set of a graph (known as 2‐dominating set) is ‐dominating; to distinguish these concepts, we define a proper ‐dominating set of a graph as follows: a subset is a proper ‐dominating set of a graph if is ‐dominating and it is not a ‐dominating set of a graph. In particular, we introduce proper ‐domination parameters and study their relations with ‐domination parameters and the classical domination numbers.