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
收藏
页码：7050 / 7057
页数：8
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