Geodesic
Effect of edge-subdivision on vertex-domination in a graph
Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 2, pp. 335-347

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

Let G be a graph with Δ(G) > 1. It can be shown that the domination number of the graph obtained from G by subdividing every edge exactly once is more than that of G. So, let ξ(G) be the least number of edges such that subdividing each of these edges exactly once results in a graph whose domination number is more than that of G. The parameter ξ(G) is called the subdivision number of G. This notion has been introduced by S. Arumugam and S. Velammal. They have conjectured that for any graph G with Δ(G) > 1, ξ(G) ≤ 3. We show that the conjecture is false and construct for any positive integer n ≥ 3, a graph G of order n with ξ(G) > [1/3]log₂ n. The main results of this paper are the following: (i) For any connected graph G with at least three vertices, ξ(G) ≤ γ(G)+1 where γ(G) is the domination number of G. (ii) If G is a connected graph of sufficiently large order n, then ξ(G) ≤ 4√n ln n+5
Keywords: domination number, subdivision number, matching 
@article{DMGT_2002_22_2_a9,
     author = {Bhattacharya, Amitava and Vijayakumar, Gurusamy},
     title = {Effect of edge-subdivision on vertex-domination in a graph},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {335--347},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2002_22_2_a9/}
}
TY  - JOUR
AU  - Bhattacharya, Amitava
AU  - Vijayakumar, Gurusamy
TI  - Effect of edge-subdivision on vertex-domination in a graph
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2002
SP  - 335
EP  - 347
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2002_22_2_a9/
LA  - en
ID  - DMGT_2002_22_2_a9
ER  - 
%0 Journal Article
%A Bhattacharya, Amitava
%A Vijayakumar, Gurusamy
%T Effect of edge-subdivision on vertex-domination in a graph
%J Discussiones Mathematicae. Graph Theory
%D 2002
%P 335-347
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2002_22_2_a9/
%G en
%F DMGT_2002_22_2_a9
Bhattacharya, Amitava; Vijayakumar, Gurusamy. Effect of edge-subdivision on vertex-domination in a graph. Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 2, pp. 335-347. http://geodesic.mathdoc.fr/item/DMGT_2002_22_2_a9/