Abstarct: In this thesis, we study 1-moved dominating in graphs. In chapter 1, we state some elementary concepts witch we use for the next chapter. In chapter 2, we study 1-moved domination in graphs and give several examples and bounds. In chapter 3, we study irredance sets in trees and several bounds for irredundance number and secure domination number. in chapter 4, we study 1-movable domination in trees.