## A note on graphs with disjoint dominating and total dominating sets.(English)Zbl 1224.05370

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.

### MSC:

 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)

### Keywords:

domination; total domination; vertex partition