Geodesic
Point-set domatic numbers of graphs
Mathematica Bohemica, Tome 124 (1999) no. 1, pp. 77-82

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MR Zbl
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.
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.
DOI : 10.21136/MB.1999.125976
Classification : 05C35, 05C69
Keywords: dominating set; point-set dominating set; point-set domatic number; bipartite graph 
Zelinka, Bohdan. Point-set domatic numbers of graphs. Mathematica Bohemica, Tome 124 (1999) no. 1, pp. 77-82. doi: 10.21136/MB.1999.125976
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