Department of Mathematics
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.
total domination number, total restrained domination number, tree
Source Publication Title
Discussiones Mathematicae Graph Theory
De Gruyter Open
Link to Publisher's Edition
Chen, Xue-Gang, Wai Chee Shiu, and Hong-Yu Chen. "Trees with equal total domination and total restrained domination numbers." Discussiones Mathematicae Graph Theory 28.1 (2008): 59-66.