Graphs with few total dominating sets

被引：2
作者：
Krzywkowski, Marcin [1 ,3 ]
Wagner, Stephan [2 ]
机构：
[1] Gdansk Univ Technol, Fac Elect Telecommun & Informat, Gdansk, Poland
[2] Stellenbosch Univ, Dept Math Sci, Stellenbosch, South Africa
[3] Univ Johannesburg, Claude Leon Fdn, Dept Pure & Appl Math, Johannesburg, South Africa
来源：
DISCRETE MATHEMATICS | 2018年 / 341卷 / 04期
基金：
新加坡国家研究基金会;
关键词：
Total dominating set; Total domination number; Subdivided star; Lower bound; TREES; NUMBER;
D O I：
10.1016/j.disc.2018.01.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a lower bound for the number of total dominating sets of a graph together with a characterization of the extremal graphs, for trees as well as arbitrary connected graphs of given order. Moreover, we obtain a sharp lower bound involving both the order and the total domination number, and characterize the extremal graphs as well. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：997 / 1009
页数：13
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