A constructive characterization of trees with equal total domination and disjunctive domination numbers

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.