Stability and some results of triple effect domination

Let G = (V,E) be a graph without isolated vertices. A subset D ⊆ V is a triple effect dominating set if every vertex in D dominates exactly three vertices of V −D. The triple effect domination number γte(G) is the minimum cardinality of overall triple effect dominating sets in G. In this paper, the triple effect domination number γte(G) is studied to be changing or not after adding or deleting edge or deleting vertex. Some conditions are put on the graph to be affected or not with several results and examples. Then, the triple effect domination and its inverse are applied on several graphs obtained from complement, join and corona operations.