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.
Discussiones Mathematicae Graph Theory
De Gruyter Open
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total domination number, total restrained domination number, tree
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.