Let G = (V(G), E(G))be a simple graph. A total dominating set D of V(G) is an interior total dominating set of G if every  is an interior vertex of G. The minimum cardinality of an interior total dominating set of G, denoted by  is called an interior total domination number of G.

In this paper, we characterize the interior total dominating sets of the join, corona, lexicographic and Cartesian products of graphs and determine the corresponding interior total domination number of these graphs.

interior domination, total domination, join, corona, lexicographic product, Cartesian product.