2008•Discussiones Mathematicae Graph TheoryRequires access

Trees with equal total and total restrained domination numbers

Hongyu Chen, Xue-gang Chen, Wai Chee Shiu

Abstract

For a graph G = (V; E), a set S V (G) is a total dominating set if it is dominating and both hSi 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 hV (G) Si 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.

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Key concepts: Dominating set, Domination analysis, Mathematics, Combinatorics, Graph, Cardinality (data modeling), Set (abstract data type), Discrete mathematics