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Induced-paired domatic numbers of graphs. (English) Zbl 1003.05078

Summary: A subset \(D\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating in \(G\), if each vertex of \(G\) either is in \(D\), or is adjacent to a vertex of \(D\). If moreover the subgraph \(\langle D\rangle\) of \(G\) induced by \(D\) is regular of degree 1, then \(D\) is called an induced-paired dominating set in \(G\). A partition of \(V(G)\), each of whose classes is an induced-paired dominating set in \(G\), is called an induced-paired domatic partition of \(G\). The maximum number of classes of an induced-paired domatic partition of \(G\) is the induced-paired domatic number of \(G\). This paper studies its properties.

MSC:

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C35 Extremal problems in graph theory
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