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In the study of mathematical chemistry and chemical graph theory, a topological index, also known as a connectivity index, is the arithmetical framework of a graph that specifies its topology and also graph invariant. These topological indices are used to model quantitative structure relationships QSARs, which are connections between the work of biological or other molecular structures and the chemical structures. This study computed the first, second, and Hyper Zagreb indices, as well as Zagreb polynomials, Redefined Zagreb indices, Randic index, ABC index, and GA index of chemical structure of Rhenium Trioxide.