Henning, Michael A.; Southey, Justin A characterization of graphs with disjoint dominating and total dominating sets. (English) Zbl 1168.05348 Quaest. Math. 32, No. 1, 119-129 (2009). Summary: A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. In this paper, we provide a constructive characterization of graphs whose vertex set can be partitioned into a dominating set and a total dominating set. Cited in 9 Documents MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) Keywords:domination; total domination; vertex partition PDF BibTeX XML Cite \textit{M. A. Henning} and \textit{J. Southey}, Quaest. Math. 32, No. 1, 119--129 (2009; Zbl 1168.05348) Full Text: DOI OpenURL