Document Type

Journal Article

Department/Unit

Department of Mathematics

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.

Publication Year

2008

Journal Title

Discussiones Mathematicae Graph Theory

Volume number

28

Issue number

1

Publisher

De Gruyter Open

First Page (page number)

59

Last Page (page number)

66

Referreed

1

DOI

10.7151/dmgt.1391

ISSN (print)

20835892

Keywords

total domination number, total restrained domination number, tree

Included in

Mathematics Commons

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