Geodesic
Weakly connected domination stable trees
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 95-100 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 05C05, 05C69
Keywords: weakly connected domination number; tree; stable graphs 
@article{CMJ_2009_59_1_a6,
     author = {Lema\'nska, Magdalena and Raczek, Joanna},
     title = {Weakly connected domination stable trees},
     journal = {Czechoslovak Mathematical Journal},
     pages = {95--100},
     year = {2009},
     volume = {59},
     number = {1},
     mrnumber = {2486618},
     zbl = {1224.05097},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a6/}
}
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Lemańska, Magdalena; Raczek, Joanna. Weakly connected domination stable trees. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 95-100. http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a6/