Network behavior in the presence of fault can be analyzed, by determining the effect of graph operations that the underlying graph G has, on the fault tolerance criteria. It is important that the domination number of graph is not modified when G is modified. A tree is a smallest connected graph that can be used in such cases. In this paper, we provide a constructive characterization of domination subdivision stable trees. © 2016 Pushpa Publishing House, Allahabad, India.