Geodesic
An upper bound on the double domination number of trees
Kragujevac Journal of Mathematics, Tome 39 (2015) no. 2, p. 133

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In a graph $G$, a vertex dominates itself and its neighbors. A set $S$ of vertices in a graph $G$ is a {\em double dominating set} if $S$ dominates every vertex of $G$ at least twice. The {\em double domination number} $\gamma_{\times2}(G)$ is the minimum cardinality of a double dominating set in $G$. The {\em annihilation number} $a(G)$ is the largest integer $k$ such that the sum of the first $k$ terms of the non-decreasing degree sequence of $G$ is at most the number of edges in $G$. In this paper, we show that for any tree $T$ of order $n\ge 2$, different from $P_4$, $\gamma_{\times2}(T)\le \frac{3a(T)+1}{2}$.
Classification : 05C69
Keywords: domination number, double dominating set, double domination number, annihilation number, tree 
J. Amjadi. An upper bound on the double domination number of trees. Kragujevac Journal of Mathematics, Tome 39 (2015) no. 2, p. 133 . http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a1/
@article{KJM_2015_39_2_a1,
     author = {J. Amjadi},
     title = {An upper bound on the double domination number of trees},
     journal = {Kragujevac Journal of Mathematics},
     pages = {133 },
     year = {2015},
     volume = {39},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a1/}
}
TY  - JOUR
AU  - J. Amjadi
TI  - An upper bound on the double domination number of trees
JO  - Kragujevac Journal of Mathematics
PY  - 2015
SP  - 133 
VL  - 39
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a1/
LA  - en
ID  - KJM_2015_39_2_a1
ER  - 
%0 Journal Article
%A J. Amjadi
%T An upper bound on the double domination number of trees
%J Kragujevac Journal of Mathematics
%D 2015
%P 133 
%V 39
%N 2
%U http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a1/
%G en
%F KJM_2015_39_2_a1