Geodesic
Upper bounds for the domination subdivision and bondage numbers of graphs on topological surfaces
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 191-204

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

For a graph property $\mathcal {P}$ and a graph $G$, we define the domination subdivision number with respect to the property $\mathcal {P}$ to be the minimum number of edges that must be subdivided (where each edge in $G$ can be subdivided at most once) in order to change the domination number with respect to the property $\mathcal {P}$. In this paper we obtain upper bounds in terms of maximum degree and orientable/non-orientable genus for the domination subdivision number with respect to an induced-hereditary property, total domination subdivision number, bondage number with respect to an induced-hereditary property, and Roman bondage number of a graph on topological surfaces.
DOI : 10.1007/s10587-013-0013-5
Classification : 05C69
Keywords: domination subdivision number; graph property; bondage number; Roman bondage number; induced-hereditary property; orientable genus; non-orientable genus 
@article{10_1007_s10587_013_0013_5,
     author = {Samodivkin, Vladimir},
     title = {Upper bounds for the domination subdivision and bondage numbers of graphs on topological surfaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {191--204},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {2013},
     doi = {10.1007/s10587-013-0013-5},
     mrnumber = {3035506},
     zbl = {1274.05364},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0013-5/}
}
TY  - JOUR
AU  - Samodivkin, Vladimir
TI  - Upper bounds for the domination subdivision and bondage numbers of graphs on topological surfaces
JO  - Czechoslovak Mathematical Journal
PY  - 2013
SP  - 191
EP  - 204
VL  - 63
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0013-5/
DO  - 10.1007/s10587-013-0013-5
LA  - en
ID  - 10_1007_s10587_013_0013_5
ER  - 
%0 Journal Article
%A Samodivkin, Vladimir
%T Upper bounds for the domination subdivision and bondage numbers of graphs on topological surfaces
%J Czechoslovak Mathematical Journal
%D 2013
%P 191-204
%V 63
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0013-5/
%R 10.1007/s10587-013-0013-5
%G en
%F 10_1007_s10587_013_0013_5
Samodivkin, Vladimir. Upper bounds for the domination subdivision and bondage numbers of graphs on topological surfaces. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 191-204. doi: 10.1007/s10587-013-0013-5

Cité par Sources :