A NOTE ON THE NUMBER OF DOMINATING SETS OF A GRAPH

被引：0
|
作者：
Wagner, Stephan [1 ]
机构：
[1] Univ Stellenbosch, Dept Math Sci, ZA-7602 Matieland, South Africa
来源：
UTILITAS MATHEMATICA | 2013年 / 92卷
基金：
新加坡国家研究基金会;
关键词：
dominating sets; lower bounds; Nordhaus-Gaddum inequality;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In a recent article by Brod and Skupien, sharp upper and lower bounds for the number of dominating sets in a tree were determined. In the present paper we show that the lower bound even holds for graphs without isolated vertices and characterise the cases of equality. Further results on this graph parameter are a Turan-type theorem for the number of dominating sets of a graph with given domination number, and a Nordhaus-Gaddum inequality.
引用
收藏
页码：25 / 31
页数：7
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