A constructive characterization of trees with equal total domination and disjunctive domination numbers. Issue 4 (4th July 2016)

• Record Type: Journal Article
• Authors: Henning, Michael A.; Marcon, Sinclair A.
• Is Part Of: Quaestiones mathematicae. Volume 39:Issue 4(2016)
• Page Start: 531
• Page End: 543
• Publication Date: 2016-07-04
• Subjects: 05C69; Domination -- disjunctive domination -- trees; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2015.1096860
• Languages: English
• ISSNs: 1607-3606

Abstract

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.