Science and Education Publishing American Journal of Applied Mathematics and Statistics 2333-4576 2 4 2014 07 28 Total Domination Subdivision Number in Strong Product Graph 216 219 EN P. Jeyanthi Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur, Tamil Nadu, India G. Hemalatha B. Davvaz AJAMS2014247 10.12691/ajams-2-4-7 2014 06 03 2014 07 25 2014 07 28 A set D of vertices in a graph G(V,E) is called a total dominating set if every vertex vV is adjacent to an element of D. The domination subdivision number of a graph G is the minimum number of edges that must be subdivided in order to increase the domination number of a graph. In this paper, we determine the total domination number for strong product graph and establish bounds on the total domination subdivision number for strong product graph.