ArticleOriginal scientific text
Title
Trees with equal restrained domination and total restrained domination numbers
Authors 1
Affiliations
- Department of Discrete Mathematics, Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland
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
Bibliography
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Pages:
83-91
Main language of publication
English
Published
2007
DOI: 10.7151/dmgt.1346
Exact and natural sciences