| Title:
|
Vertices contained in all minimum paired-dominating sets of a tree (English) |
| Author:
|
Chen, Xue-Gang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
407-417 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A set $S$ of vertices in a graph $G$ is called a paired-dominating set if it dominates $V$ and $\langle S\rangle $ contains at least one perfect matching. We characterize the set of vertices of a tree that are contained in all minimum paired-dominating sets of the tree. (English) |
| Keyword:
|
domination number |
| Keyword:
|
paired-domination number |
| Keyword:
|
tree |
| MSC:
|
05C05 |
| MSC:
|
05C35 |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 1174.05090 |
| idMR:
|
MR2309974 |
| . |
| Date available:
|
2009-09-24T11:46:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128180 |
| . |
| Reference:
|
[1] P. L. Hammer, P. Hansen and B. Simeone: Vertices belonging to all or to no maximum stable sets of a graph.SIAM J. Algebraic Discrete Math. 3 (1982), 511–522. MR 0679645, 10.1137/0603052 |
| Reference:
|
[2] C. M. Mynhardt: Vertices contained in every minimum dominating set of a tree.J. Graph Theory 31 (1999), 163–177. Zbl 0931.05063, MR 1688945, 10.1002/(SICI)1097-0118(199907)31:3<163::AID-JGT2>3.0.CO;2-T |
| Reference:
|
[3] E. J. Cockayne, M. A. Henning and C. M. Mynhardt: Vertices contained in all or in no minimum total dominating set of a tree.Discrete Math. 260 (2003), 37–44. MR 1948372, 10.1016/S0012-365X(02)00447-8 |
| Reference:
|
[4] T. W. Haynes and P. J. Slater: Paired-domination in graphs.32 (1998), Networks, 199–206. MR 1645415 |
| Reference:
|
[5] T. W. Haynes, M. A. Henning and P. J. Slater: Strong equality of domination parameters in trees.Discrete Math. 260 (2003), 77–87. MR 1948376, 10.1016/S0012-365X(02)00451-X |
| Reference:
|
[6] T. W. Haynes, S. T. Hedetniemi and P. J. Slater: Fundamentals of Domination in Graphs.Marcel Dekker, New York, 1998. MR 1605684 |
| Reference:
|
[7] : Domination in Graphs: Advanced Topics.T. W. Haynes, S. T. Hedetniemi and P. J. Slater (eds.), Marcel Dekker, New York, 1998. Zbl 0883.00011, MR 1605685 |
| . |
