Geodesic
Domination Number, Independent Domination Number and 2-Independence Number in Trees
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 39-49

Voir la notice de l'article provenant de la source Library of Science

For a graph G, let γ(G) be the domination number, i(G) be the independent domination number and β_2(G) be the 2-independence number. In this paper, we prove that for any tree T of order n ≥ 2, 4β_2(T) − 3γ(T) ≥ 3i(T), and we characterize all trees attaining equality. Also we prove that for every tree T of order n ≥ 2, i(T)≤3β_2(T)/4, and we characterize all extreme trees.
Keywords: 2-independence number, domination number, independent domination number 
@article{DMGT_2021_41_1_a1,
     author = {Dehgardi, Nasrin and Sheikholeslami, Seyed Mahmoud and Valinavaz, Mina and Aram, Hamideh and Volkmann, Lutz},
     title = {Domination {Number,} {Independent} {Domination} {Number} and {2-Independence} {Number} in {Trees}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {39--49},
     publisher = {mathdoc},
     volume = {41},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a1/}
}
TY  - JOUR
AU  - Dehgardi, Nasrin
AU  - Sheikholeslami, Seyed Mahmoud
AU  - Valinavaz, Mina
AU  - Aram, Hamideh
AU  - Volkmann, Lutz
TI  - Domination Number, Independent Domination Number and 2-Independence Number in Trees
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2021
SP  - 39
EP  - 49
VL  - 41
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a1/
LA  - en
ID  - DMGT_2021_41_1_a1
ER  - 
%0 Journal Article
%A Dehgardi, Nasrin
%A Sheikholeslami, Seyed Mahmoud
%A Valinavaz, Mina
%A Aram, Hamideh
%A Volkmann, Lutz
%T Domination Number, Independent Domination Number and 2-Independence Number in Trees
%J Discussiones Mathematicae. Graph Theory
%D 2021
%P 39-49
%V 41
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a1/
%G en
%F DMGT_2021_41_1_a1
Dehgardi, Nasrin; Sheikholeslami, Seyed Mahmoud; Valinavaz, Mina; Aram, Hamideh; Volkmann, Lutz. Domination Number, Independent Domination Number and 2-Independence Number in Trees. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 39-49. http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a1/