Repozytorium publikacji - Politechnika Gdańska

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Repozytorium publikacji
Politechniki Gdańskiej

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On proper (1,2)‐dominating sets in graphs

In 2008, Hedetniemi et al. introduced the concept of (1,)-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 is a proper (1,2) -dominating set of a graph if 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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