| Title:
|
Weakly connected domination stable trees (English) |
| Author:
|
Lemańska, Magdalena |
| Author:
|
Raczek, Joanna |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
95-100 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A dominating set $D\subseteq V(G)$ is a {\it weakly connected dominating set} in $G$ if the subgraph $G[D]_w=(N_G[D],E_w)$ weakly induced by $D$ is connected, where $E_w$ is the set of all edges having at least one vertex in $D$. {\it Weakly connected domination number} $\gamma _w(G)$ of a graph $G$ is the minimum cardinality among all weakly connected dominating sets in $G$. A graph $G$ is said to be {\it weakly connected domination stable} or just $\gamma _w$-{\it stable} if $\gamma _w(G)=\gamma _w(G+e)$ for every edge $e$ belonging to the complement $\overline G$ of $G.$ We provide a constructive characterization of weakly connected domination stable trees. (English) |
| Keyword:
|
weakly connected domination number |
| Keyword:
|
tree |
| Keyword:
|
stable graphs |
| MSC:
|
05C05 |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 1224.05097 |
| idMR:
|
MR2486618 |
| . |
| Date available:
|
2010-07-20T14:54:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140466 |
| . |
| Reference:
|
[1] Sumner, D. P., Blitch, P.: Domination critical graphs.J. Combin. Theory Ser. B 34 (1983), 65-76. Zbl 0512.05055, MR 0701172, 10.1016/0095-8956(83)90007-2 |
| Reference:
|
[2] Dunbar, J. E., Grossman, J. W., Hattingh, J. H., Hedetniemi, S. T., McRae, A.: On weakly-connected domination in graphs.Discrete Mathematics 167-168 (1997), 261-269. Zbl 0871.05037, MR 1446750 |
| Reference:
|
[3] Henning, M. A.: Total domination excellent trees.Discrete Mathematics 263 (2003), 93-104. Zbl 1015.05065, MR 1955717, 10.1016/S0012-365X(02)00572-1 |
| Reference:
|
[4] Chen, X., Sun, L., Ma, D.: Connected domination critical graphs.Applied Mathematics Letters 17 (2004), 503-507. Zbl 1055.05110, MR 2057342, 10.1016/S0893-9659(04)90118-8 |
| Reference:
|
[5] Lemańska, M.: Domination numbers in graphs with removed edge or set of edges.Discussiones Mathematicae Graph Theory 25 (2005), 51-56. MR 2152049, 10.7151/dmgt.1259 |
| . |
