The molecular topology of a graph is described by topological indices, which are numerical measures. In theoretical chemistry, topological indices are numerical quantities that are used to represent the molecular topology of networks. These topological indices can be used to calculate several physical and chemical properties of chemical compounds, such as boiling point, entropy, heat generation, and vaporization enthalpy. Graph theory comes in handy when looking at the link between certain topological indices of some derived graphs. In the ongoing research, we determine ve-degree, ev-degree, and degree-based (D-based) topological indices of fenofibrate's chemical structure. These topological indices are the Zagreb index, general Randic index, modified Zagreb index, and forgotten topological index. These indices are very helpful to study the characterization of the given structure.