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

被引：7

作者：

Michalski, Adrian ^{[1
]}

Wloch, Iwona ^{[1
]}

Dettlaff, Magda ^{[2
]}

Lemanska, Magdalena ^{[2
]}

机构：

[1] Rzeszow Univ Technol, Fac Math & Appl Phys, Dept Discrete Math, Al Powstancow Warszawy 8, PL-35959 Rzeszow, Poland

[2] Gdansk Univ Technol, Fac Appl Phys & Math, Inst Appl Math, Gdansk, Poland

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2022年 / 45卷 / 11期

关键词：

(1,2)-dominating set; dominating set; domination numbers; proper (1,2)-dominating set; INDEPENDENCE; NUMBER; (2-D)-KERNELS; 2-DOMINATION; EXISTENCE;

D O I：

10.1002/mma.8223

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：7050 / 7057

页数：8

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