| Title:
|
Antidomatic number of a graph (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
191-195 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called dominating in $G$, if for each $x\in V(G)-D$ there exists $y\in D$ adjacent to $x$. An antidomatic partition of $G$ is a partition of $V(G)$, none of whose classes is a dominating set in $G$. The minimum number of classes of an antidomatic partition of $G$ is the number $\bar{d} (G)$ of $G$. Its properties are studied. (English) |
| Keyword:
|
dominating set |
| Keyword:
|
antidomatic partition |
| Keyword:
|
antidomatic number |
| MSC:
|
05C35 |
| idZBL:
|
Zbl 0909.05031 |
| idMR:
|
MR1478772 |
| . |
| Date available:
|
2008-06-06T21:33:19Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107610 |
| . |
| Reference:
|
[1] Cockayne, E. J., Redetniemi, S. T.: Towards a theory of domination in graphs.Networks 7(1977), 247–261. MR 0483788 |
| Reference:
|
[2] Zelinka, B.: Some numerical invariants of graphs.DrSc dissertation, Charles University, Prague 1988 (Czech). |
| . |
