Trees with equal total domination and total restrained domination numbers

Xue-Gang Chen, Wai Chee Shiu, Hong-Yu Chen

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)59-66
JournalDiscussiones Mathematicae Graph Theory
Volume28
Issue number1
DOIs
Publication statusPublished - 2008

User-Defined Keywords

  • total domination number
  • total restrained domination number
  • tree

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