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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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