Total Domination on Tree Operators

Let G be a graph with vertex set V and edge set E , a set D⊆ V is a total dominating set if every vertex v∈ V has at least one neighbor in D . The minimum cardinality among all total dominating sets is called the total domination number, and it is denoted by γ _t(G) . Given an arbitrary tree graph T , we consider some operators acting on this graph; (T),(T),(T) and (T) , and we give bounds of the total domination number of these new graphs using other parameters in the graph T . We also give the exact value of the total domination number in some of them.