Bounds on the energy of a graph and its relation with topological indices

In this paper, we provide the upper bound on the energy of a graph using the Diaz-metcalf inequality. Then, we obtained several bounds on the energy of a graph with given invariants such as order, size, diameter, radius, girth, kirchoff index, clique number, algebraic connectivity, vertex connectivity, index, etc. Finally, we obtain several bounds on the energy of a graph in terms of many topological indices such as harmonic index, symmetric division degree index and modified second Zagreb indices.