# Point-set domatic numbers of graphs

Mathematica Bohemica (1999)

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

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## Abstract

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

## How to cite

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

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.},
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
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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1. Cockayne E. J., Hedetniemi S. T., 10.1002/net.3230070305, Networks 7 (1977), 247-261. (1977) MR0483788DOI10.1002/net.3230070305
2. Haynes T. W., Hedetniemi S. T., Slater P. J., Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998. (1998) Zbl0890.05002MR1605684
3. Pushpa Latha L., The global point-set domination number of a graph, Indian J. Pure Appl. Math. 28 (1997), 47-51, (1997) Zbl0871.05036MR1442817
4. Sampathkumar E., Pushpa Latha L., Point-set domination number of a graph, Indian J. Pure Appl. Math. 24 (1993), 225-229. (1993) Zbl0772.05055MR1218532
5. 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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