Henning, Michael A.; Southey, Justin A note on graphs with disjoint dominating and total dominating sets. (English) Zbl 1224.05370 Ars Comb. 89, 159-162 (2008). Summary: 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 note, we show that the vertex set of every graph with minimum degree at least two and with no component that is a 5-cycle can be partitioned into a dominating set and a total dominating set. Cited in 3 ReviewsCited in 12 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}, Ars Comb. 89, 159--162 (2008; Zbl 1224.05370) OpenURL