A topological descriptor is a mathematical illustration of a molecular construction that relates particular
physicochemical properties of primary molecular structure as well as its mathematical depiction. Topological
co-indices are usually applied for quantitative structure action relationships (QSAR) and quantitative structure
property relationships (QSPR). Topological co-indices are topological descriptor which consider the noncontiguous
vertex set. In this study, we studyied some of the accompanied renowned topological co-indices: the 1st and
2nd Zagreb co-indices, the 1st and 2nd multiplicative Zagreb co-indices, and the F-coindex. By applying structure
based examinations and deductions, we discuss the earlier stated co-indices of few synthetic atomic structures
that are frequently used in clinical, synthetic, and material designing.