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Upper bounds for the domination subdivision and bondage numbers of graphs on topological surfaces

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 de…