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Graphs with disjoint dominating and paired-dominating sets. (English) Zbl 1215.05126

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 paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains a perfect matching. In this paper, we show that no minimum degree is sufficient to guarantee the existence of a disjoint dominating set and a paired-dominating set. However, we prove that the vertex set of every cubic graph can be partitioned into a dominating set and a paired-dominating set.

MSC:

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