A topological index is a type of molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are used for example in the development of QSAR QSPR in which the biological activity or other properties of molecules are correlated with their chemical structure. In this paper, we establish several inequalities among the molecular descriptors such as the generalized version of the first Zagreb index, the Randić index, the ABC index, AZI index, and the redefined first, second and third Zagreb indices.