eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2333-4576 2014-07-28 2 4 216 219 10.12691/ajams-2-4-7 AJAMS2014247 article P. Jeyanthi jeyajeyanthi@rediffmail.com 1 G. Hemalatha 2 B. Davvaz 3 Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur, Tamil Nadu, India Department of mathematics, Shri Andal Alagar College of Engineering, Mamandur, Kancheepuram, Tamil Nadu, India Department of Mathematics, Yazd University, Yazd, Iran 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. http://pubs.sciepub.com/ajams/2/4/7/ajams-2-4-7.pdf total dominating set strong product graph total domination number