Discussiones Mathematicae Graph Theory 27(1) (2007) 83-91
doi: 10.7151/dmgt.1346

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TREES WITH EQUAL RESTRAINED DOMINATION AND TOTAL RESTRAINED DOMINATION NUMBERS

Joanna Raczek

Department of Discrete Mathematics
Faculty of Applied Physics and Mathematics

Gdańsk University of Technology
Narutowicza 11/12, 80-952 Gdańsk, Poland
e-mail: gardenia@pg.gda.pl

Abstract

For a graph G = (V,E), a set D ⊆ V(G) is a total restrained dominating set if it is a dominating set and both ⟨D ⟩ and ⟨V(G)−D⟩ do not have isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. A set D ⊆ V(G) is a restrained dominating set if it is a dominating set and ⟨V(G)−D ⟩ does not contain an isolated vertex. The cardinality of a minimum restrained dominating set in G is the restrained domination number. We characterize all trees for which total restrained and restrained domination numbers are equal.

Keywords: total restrained domination number, restrained domination number, trees.

2000 Mathematics Subject Classification: 05C05, 05C69.

References

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Received 7 November 2005
Revised 21 August 2006