A constructive characterization of trees with equal total domination and disjunctive domination numbers. Issue 4 (4th July 2016) - Henning, Michael A.; Marcon, Sinclair A.
Abstract: A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to a vertex in S . The total domination number, γt ( G ), of G is the minimum cardinality of a total dominating set of G . A set S of vertices in G is a disjunctive dominating set in G if every vertex not in S is adjacent to a vertex of S or has at least two vertices in S at distance 2 from it in G . The disjunctive domination number, ( G ), of G is the minimum cardinality of a disjunctive dominating set in G . By definition, we have ( T )≤ γt ( T ). In this paper, we provide a constructive characterization of the trees T achieving equality in this bound.