Weakly connected domination stable trees
Magdalena Lemańska; Joanna Raczek
Czechoslovak Mathematical Journal (2009)
- Volume: 59, Issue: 1, page 95-100
- ISSN: 0011-4642
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topLemańska, Magdalena, and Raczek, Joanna. "Weakly connected domination stable trees." Czechoslovak Mathematical Journal 59.1 (2009): 95-100. <http://eudml.org/doc/37910>.
@article{Lemańska2009,
abstract = {A dominating set $D\subseteq V(G)$ is a 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 $D$. 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 weakly connected domination stable or just $\gamma _w$-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.},
author = {Lemańska, Magdalena, Raczek, Joanna},
journal = {Czechoslovak Mathematical Journal},
keywords = {weakly connected domination number; tree; stable graphs; weakly connected domination number; tree; stable graph},
language = {eng},
number = {1},
pages = {95-100},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weakly connected domination stable trees},
url = {http://eudml.org/doc/37910},
volume = {59},
year = {2009},
}
TY - JOUR
AU - Lemańska, Magdalena
AU - Raczek, Joanna
TI - Weakly connected domination stable trees
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 95
EP - 100
AB - A dominating set $D\subseteq V(G)$ is a 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 $D$. 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 weakly connected domination stable or just $\gamma _w$-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.
LA - eng
KW - weakly connected domination number; tree; stable graphs; weakly connected domination number; tree; stable graph
UR - http://eudml.org/doc/37910
ER -
References
top- Sumner, D. P., Blitch, P., 10.1016/0095-8956(83)90007-2, J. Combin. Theory Ser. B 34 (1983), 65-76. (1983) Zbl0512.05055MR0701172DOI10.1016/0095-8956(83)90007-2
- 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. (1997) Zbl0871.05037MR1446750
- Henning, M. A., 10.1016/S0012-365X(02)00572-1, Discrete Mathematics 263 (2003), 93-104. (2003) Zbl1015.05065MR1955717DOI10.1016/S0012-365X(02)00572-1
- Chen, X., Sun, L., Ma, D., 10.1016/S0893-9659(04)90118-8, Applied Mathematics Letters 17 (2004), 503-507. (2004) Zbl1055.05110MR2057342DOI10.1016/S0893-9659(04)90118-8
- Lemańska, M., 10.7151/dmgt.1259, Discussiones Mathematicae Graph Theory 25 (2005), 51-56. (2005) MR2152049DOI10.7151/dmgt.1259
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