In Sri Lanka as well as the rest of the globe, cancer is the top cause of mortality. One of the key medicines in treating tumors is anticancer medications and delivery dendrimers. To prevent the formation of the rapid proliferation of cancer cells, several tests were carried out. Because of this, research on dendrimers and anti-cancer medications is crucial. Topological indices (TIs) are molecular descriptors numerical values corresponding to the physical characteristics of a molecule’s chemical structure. It costs money to determine a molecule’s physical characteristics in a lab since it takes a lot of materials, medications, and time. Therefore, the relevant information about molecules may be obtained by computing TIs. This study’s goals are to compute hitherto uncalculated eccentricity-based TIs for various anticancer structures and to use curvilinear regression models to forecast the physical characteristics of particular anticancer medications. These anticancer medications were given different TIs developed in this work, allowing the researchers to understand the physical, physicochemical, and chemical characteristics related to them. In addition comparative study of the novel indices with some well-known and mostly used indices in structure–property modeling and anticancer drugs in performed.