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Vertex covering transversal domatic number of graphs. (English) Zbl 1371.05222
Summary: A dominating set $$S \subseteq V$$ in a simple graph $$G=(V,E)$$ is said to be a vertex covering transversal dominating set if it intersects every minimum vertex covering set of $$G$$. The vertex covering transversal domination number $$\gamma_{\mathrm{vct}}(G)$$ is the minimum cardinality among all vertex covering transversal dominating sets of $$G$$. A partition $$\{V_1,V_2,\ldots,V_k\}$$ of $$V$$ is called a vertex covering transversal domatic partition of $$G$$ if each $$V_i$$ is a vertex covering transversal dominating set. The maximum cardinality of a vertex covering transversal domatic partition of $$G$$ is called the vertex covering transversal domatic number of $$G$$ and is denoted by $$d_{\mathrm{vct}}(G)$$. In this paper, we analyze this parameter for some standard graphs and also obtain its bounds.

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