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Human immune deficiency virus (HIV), a retrovirus, is the main reason for acquired immune deficiency syndrome (AIDS), and one of the prime social and medical problems at the present time. Approximately around 100 million citizens all over the world are suffering from HIV virus and around 50 million citizens are dead. This virus expanded rapidly all over the world. Unfortunately, there is no medicine, drug or vaccine is identified to treat this virus. Scientists have recognised the effectiveness of already existing anti-viral drugs to cure and control the HIV virus. Some of them are Tri-POC Tenofovir Dimer, Tenofovir Disproxil and Tenofovir Alafenamide.Topological indices- mathematical elucidations for a molecule can be created by an algorithm and can be applied to its representation. To generate various biological and physicochemical properties of chemical compounds, topological indices are used. In the current study, by using polynomial approach, for the above mentioned antiviral drugs, certain neighbourhood sum& degree based topological indices have been studied. The outcomes achieved can support the invention of new medicine for the cure of AIDS. In the present study, we establish some topological properties of Tenofovir dimer, Tenofovir disproxil and alafenamide used to inhibit the outbreak of AIDS. We compute some topological indices (general indices (Randic and harmonic), Zagreb index (1st, 2nd, 3rd, second modified, Redefined 3rdand Augmented), Forgotten index, Systematic division index and Inverse sum indices for these three chemical structures. In Medical Science, topological index calculation defines the topological index related to molecular structure and its corresponding biological, medical, pharmaceutical, and chemical properties of the medicines. From last twenty to thirty years the world is fronting the danger of identifying cure for AIDS. Nearly 10 million people are getting affected with this disease every year. In order to cure this malicious disease antiviral drugs, in form of anti-metabolites, hormones and alkylating agents are used. As per numerous examinations conducted with their chemical structures, it revealed that there is a association between the characteristic features of these anti-viral medicines, drugs and alkane’s viz.enthalpy, melting point and boiling point. In this current study, numerous topological indices have been defined on few of the above mentioned drugs so as to assist the scientists to identify the chemical reactions and physical & chemical characteristics and biological activities that are related with them. Hence, the topological indices study on the molecular structure of the medicines, drugs chemical compounds, can constitute for absence of laboratory research which provides a notional origin for the production of chemical materials and drugs. In the present study, we analysed the Tenofovir family chemicals which is extensively used in antiviral medicines and drugs invention. Eleven topological indices are analysed using multi-order polynomials and these results can be used in medicine and pharmaceutical experiments thus paving the new way for new drug invention for AIDS.