| Title:
|
Point-set domatic numbers of graphs (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
77-82 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
dominating set |
| Keyword:
|
point-set dominating set |
| Keyword:
|
point-set domatic number |
| Keyword:
|
bipartite graph |
| MSC:
|
05C35 |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 0933.05112 |
| idMR:
|
MR1687413 |
| DOI:
|
10.21136/MB.1999.125976 |
| . |
| Date available:
|
2009-09-24T21:35:17Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125976 |
| . |
| Reference:
|
[1] Cockayne E. J., Hedetniemi S. T.: Towards the theory of domination in graphs.Networks 7 (1977), 247-261. MR 0483788, 10.1002/net.3230070305 |
| Reference:
|
[2] Haynes T. W., Hedetniemi S. T., Slater P. J.: Fundamentals of Domination in Graphs.Marcel Dekker, Inc., New York, 1998. Zbl 0890.05002, MR 1605684 |
| Reference:
|
[3] Pushpa Latha L.: The global point-set domination number of a graph.Indian J. Pure Appl. Math. 28 (1997), 47-51, Zbl 0871.05036, MR 1442817 |
| Reference:
|
[4] Sampathkumar E., Pushpa Latha L.: Point-set domination number of a graph.Indian J. Pure Appl. Math. 24 (1993), 225-229. Zbl 0772.05055, MR 1218532 |
| Reference:
|
[5] Sampathkumar E., Pushpa Latha L.: Set domination in graphs.J. Graph Theory 18 (1994), 489-495. Zbl 0807.05066, MR 1283314, 10.1002/jgt.3190180507 |
| . |
