On Proper 2-Dominating Sets in Graphs

被引：3
作者：
Bednarz, Pawel [1 ]
Pirga, Mateusz [1 ]
机构：
[1] Rzeszow Univ Technol, Fac Math & Appl Phys, Al Powstancow Warszawy 12, PL-35959 Rzeszow, Poland
来源：
SYMMETRY-BASEL | 2024年 / 16卷 / 03期
关键词：
dominating set; 2-dominating set; 3-dominating set; proper 2-dominating set; DOUBLE DOMINATION; KERNELS; NUMBER; (2-D)-KERNELS; PATHS;
D O I：
10.3390/sym16030296
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
This paper introduces the concept of proper 2-dominating sets in graphs, providing a comprehensive characterisation of graphs that possess such sets. We give the necessary and sufficient conditions for a graph to have a proper 2-dominating set. Graphs with proper dominating sets can have a symmetric structure. Moreover, we estimate the bounds of the proper 2-domination number in the graphs with respect to the 2-domination and 3-domination numbers. We show that the cardinality of gamma 2 over bar -set is greater by one at most than the cardinality of gamma 2-set.
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页数：10
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