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Keywords:
dominating set; point-set dominating set; point-set domatic number; bipartite graph
dominating set; point-set dominating set; point-set domatic number; bipartite graph
Summary:
A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called point-set dominating, if for each subset $S\subseteq V(G)-D$ there exists a vertex $v\in D$ such that the subgraph of $G$ induced by $S\cup\{v\}$ is connected. The maximum number of classes of a partition of $V(G)$, all of whose classes are point-set dominating sets, is the point-set domatic number $d_p(G)$ of $G$. Its basic properties are studied in the paper.
References:
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