Abstarct: Several matrices can be associated to a graph such as the adjacency matrix or the Laplacian matrix. The spectrum of these matrices gives some information about the structure of the graph. In this thesis, we introduce and study the concepts of double dominating energy of some graphs, Laplacian minimum dominating energy of some graphs and also double dominating Laplacian energy of some graphs. Calculating the above energies in graphs, we present some bounds for each of these energies and also consider their structural properties.