On the Ratio Between 2-Domination and Total Outer-Independent Domination Numbers of Trees

A 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V（G） ／ D has at least two neighbors in D. A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V（G） ／ D is independent. The...

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Bibliographic Details
Published in:Chinese annals of mathematics. Serie B 2013-09, Vol.34 (5), p.765-776
Main Author: Krzywkowski, Marcin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
控制数
支配集
曲线图
比例
独立控制
邻居
集合
顶点
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Summary:A 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V（G） ／ D has at least two neighbors in D. A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V（G） ／ D is independent. The 2-domination （total outer-independent domination, respectively） number of a graph G is the minimum cardinality of a 2-dominating （total outer-independent dominating, respectively） set of G. We investigate the ratio between 2-domination and total outer-independent domination numbers of trees.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-013-0788-6