Some degree-based topological indices and (normalized Laplacian) energy of graphs

In this paper, by utilizing the concept of the energy of a vertex, connections between some vertex-degree-based topological indices (including the general Randic index, the first Zagreb index, and the forgotten index) and the energy of graphs are established. Several bounds on the energy of the graphs containing no isolated vertices are also given in terms of the first Zagreb index and the forgotten index. Moreover, bounds on the normalized Laplacian energy in terms of two particular cases of the general Randic index are obtained.