Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

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

total domination number, total restrained domination number, tree

Publication Date

2008

Source Publication Title

Discussiones Mathematicae Graph Theory

Volume

28

Issue

1

Start Page

59

End Page

66

Publisher

De Gruyter Open

Peer Reviewed

1

DOI

10.7151/dmgt.1391

Link to Publisher's Edition

http://dx.doi.org/10.7151/dmgt.1391

ISSN (print)

20835892

Included in

Mathematics Commons

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