Topological Indices (TIs) have been proposed as the particular type of molecular descriptors. These indices can determine the existing relations between different properties of an organic compound or molecular structures at the Nano scale. In this research, after reviewing the TIs that have been proposed during the last 10 years to describe the relationship between physical-chemical properties of molecular structures, their capability to reveal the properties of a nanostructure and analysis of construction with the process of their synthesis, have been investigated. Also, by focusing on the Geometric-Arithmetic (GA) topological index, mathematical properties of the edge GA index obtained using techniques available in graph theory. Then we extended these properties on the available Nano-star and Nano-tubes like TUC4C8(R) and TUC4C8 (S). In addition, we proposed an algorithm for computing of the edge GA index with the use of mathematical properties of molecular graphs. By using computer calculation on some numerical examples, the results of GA indices have been examined if the precision of describing the molecular properties were accurate. Nowadays, the structures such as QSAR and QSPR which are the laboratory medium in the field of nanotechnology, work on the basis of molecular descriptors including topological indices. In this research, we showed that computing of GA indices for different molecular graphs can have a high impact to provide QSAR and QSPR. On the other hand, we have tried to propose a rapid calculation method for different types of GA indices. This method makes it possible to run GA on numerous structures, and thus it can be used as a specific feature in Nano-related science for a variety of fields such as healthcare, industry and Pharmacology. Our future research will be based on the improvement and development of the proposed computing environment in this study. Therefore, we can use the results of national and international researches introduced topological indices, for simulating and making molecular structures such as laboratory medium, drug carriers, Nano-biotechnology sensors and etc.