In 2008, Hedetniemi et al. introduced the concept of (1,k)‐domination and obtained some interesting results for (1,2) ‐domination. Obviously every (1,1) ‐dominating set of a graph (known as 2‐dominating set) is (1,2) ‐dominating; to distinguish these concepts, we define a proper (1,2) ‐dominating set of a graph as follows: a subset D is a proper (1,2) ‐dominating set of a graph if D is (1,2) ‐dominating and it is not a (1,1) ‐dominating set of a graph. In particular, we introduce proper (1,2) ‐domination parameters and study their relations with (1,2) ‐domination parameters and the classical domination numbers.
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