Abstarct: In this thesis, we will study some properties of distance energy of a graph G. frist, we have graph energy and some of graph energy of bounds, also we have Laplacian energy then we will review bounds of Laplacian energy, Second bounds of distance energy will be detected. In the following, we will survey minimum covering distance energy and it’s bounds then, we will comput minimum covering distance energy of some of standard graphs such as complete graph, crown graph, star graph and biparite graph, Also we will review minimum dominating distance energy and upper and lower bound’s, we will comput minimum dominating distance energy of a few standard graphs like complete graph, crown graph, star graph. Finally, the end of thesis is related to distance Laplacian minimum covering energy that we could catch a bound for it and distance Laplacian minimum covering energy complete graph and star graph which is developed in an innovative way.