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.

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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 
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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. http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0013-5/

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