Total Domination on Tree Operators

Abstract

Let G be a graph with vertex set V and edge set E, a set Dsubseteq V is a total dominating set if every vertex vin 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 gamma _{t}(G). Given an arbitrary tree graph T, we consider some operators acting on this graph; texttt {S}(T),texttt {R}(T),texttt {Q}(T) and texttt {T}(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.