| Title:
|
Induced-paired domatic numbers of graphs (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
591-596 |
| 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 each vertex of $G$ either is in $D$, or is adjacent to a vertex of $D$. If moreover the subgraph $<D>$ of $G$ induced by $D$ is regular of degree 1, then $D$ is called an induced-paired dominating set in $G$. A partition of $V(G)$, each of whose classes is an induced-paired dominating set in $G$, is called an induced-paired domatic partition of $G$. The maximum number of classes of an induced-paired domatic partition of $G$ is the induced-paired domatic number $d_{\text{ip}}(G)$ of $G$. This paper studies its properties. (English) |
| Keyword:
|
dominating set |
| Keyword:
|
induced-paired dominating set |
| Keyword:
|
induced-paired domatic number |
| MSC:
|
05C35 |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 1003.05078 |
| idMR:
|
MR1942644 |
| DOI:
|
10.21136/MB.2002.133954 |
| . |
| Date available:
|
2009-09-24T22:05:32Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133954 |
| . |
| Reference:
|
[1] E. J. Cockayne, S. T. Hedetniemi: Towards a theory of domination in graphs.Networks 7 (1977), 247–261. MR 0483788, 10.1002/net.3230070305 |
| Reference:
|
[2] T. W. Haynes, S. T. Hedetniemi, P. J. Slater: Fundamentals of Domination in Graphs.Marcel Dekker, New York, 1998. MR 1605684 |
| Reference:
|
[3] D. S. Studer, T. W. Haynes, L. M. Lawson: Induced-paired domination in graphs.Ars Combinatoria 57 (2000), 111–128. MR 1796633 |
| Reference:
|
[4] B. Zelinka: Adomatic and idomatic numbers of graphs.Math. Slovaca 33 (1983), 99–103. Zbl 0507.05059, MR 0689285 |
| . |
