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A characterization of graphs with disjoint dominating and total dominating sets. (English) Zbl 1168.05348

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.

MSC:

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