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ArticleOriginal scientific text

Title

Trees with equal total domination and total restrained domination numbers

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, North China Electric Power University, Beijing 102206, China
  2. Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China
  3. The College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, Shandong Province 266510, China

Abstract

For a graph G = (V,E), a set S ⊆ V(G) is a total dominating set if it is dominating and both ⟨S⟩ has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number. A set S ⊆ V(G) is a total restrained dominating set if it is total dominating and ⟨V(G)-S⟩ has no isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. We characterize all trees for which total domination and total restrained domination numbers are the same.

Keywords

ENG
total domination number, total restrained domination number, tree

Bibliography

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Discussiones Mathematicae Graph Theory
2008/28/1
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Pages:
59-66
Main language of publication
English
Received
2006-09-22
Accepted
2007-01-24
Published
2008

DOI: 10.7151/dmgt.1391

Exact and natural sciences