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 language | English |
|---|---|
| Pages (from-to) | 59-66 |
| Number of pages | 8 |
| Journal | Discussiones Mathematicae - Graph Theory |
| Volume | 28 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2008 |
User-Defined Keywords
- total domination number
- total restrained domination number
- tree