# Point-set domatic numbers of graphs

Mathematica Bohemica (1999)

- Volume: 124, Issue: 1, page 77-82
- ISSN: 0862-7959

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topZelinka, Bohdan. "Point-set domatic numbers of graphs." Mathematica Bohemica 124.1 (1999): 77-82. <http://eudml.org/doc/248451>.

@article{Zelinka1999,

abstract = {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 \lbrace v\rbrace $ 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.},

author = {Zelinka, Bohdan},

journal = {Mathematica Bohemica},

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},

language = {eng},

number = {1},

pages = {77-82},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Point-set domatic numbers of graphs},

url = {http://eudml.org/doc/248451},

volume = {124},

year = {1999},

}

TY - JOUR

AU - Zelinka, Bohdan

TI - Point-set domatic numbers of graphs

JO - Mathematica Bohemica

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 124

IS - 1

SP - 77

EP - 82

AB - 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 \lbrace v\rbrace $ 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.

LA - eng

KW - dominating set; point-set dominating set; point-set domatic number; bipartite graph; dominating set; point-set dominating set; point-set domatic number; bipartite graph

UR - http://eudml.org/doc/248451

ER -

## References

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- Haynes T. W., Hedetniemi S. T., Slater P. J., Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998. (1998) Zbl0890.05002MR1605684
- Pushpa Latha L., The global point-set domination number of a graph, Indian J. Pure Appl. Math. 28 (1997), 47-51, (1997) Zbl0871.05036MR1442817
- Sampathkumar E., Pushpa Latha L., Point-set domination number of a graph, Indian J. Pure Appl. Math. 24 (1993), 225-229. (1993) Zbl0772.05055MR1218532
- Sampathkumar E., Pushpa Latha L., 10.1002/jgt.3190180507, J. Graph Theory 18 (1994), 489-495. (1994) Zbl0807.05066MR1283314DOI10.1002/jgt.3190180507

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