Chemical characteristics of molecules are closely related to their structures. Molecular structures have been studied by the topological indices for the last forty years. The degreebased topological indices are the most studied and commonly used topological indices, which play a significant role in characterizing molecular structures. Dendrimers have been used in cancer therapy for the last few years. This research focused on calculating the different versions of the Zagreb index and the Randić index of two well-known dendrimers which are used in cancer therapy.
Zagreb and Randić indices are the most commonly used degree-based topological indices in the study of drug design and development. In molecular topology, M-polynomials are also used to calculate the degree-based topological indices of chemical structures. In this paper, we derive the M-polynomials for the PEG-cored PAMAM, carbosilane, and poly (lysine) dendrimers and calculate their first, second, and second modified Zagreb indices and the Randić index.
The topological index is a numerical representation of a molecular structure. In chemical graphs, the atoms and the chemical bonds between them are represented by vertices and edges respectively. Vertex degree based topological indices are the most studied and mostly used type of topological indices. The mostly used vertex degree based topological indices in the field of drug design and developments are the Zagreb index and the Randić index. The structural chemistry of dendrimers could be manipulated by their topological indices to get the specific structure with required properties to deliver the drugs to target carrier vehicle. In this work, topological indices of three types of dendrimers which are used as the drug delivery system were studied and their Zagreb index and the Randić index were calculated using molecular graph theory. Moreover, the other versions of these two indices were also calculated to these dendrimers.
Buckyball, a 60 C molecule, is highly symmetric closed cage structure with a 60 number of carbon atoms and the diameter of 0.78 nanometers. This is formed by twelve pentagons and twenty hexagons that are linked by single and double carbon-carbon bonds. In this paper, we derive the M-polynomial for the Buckyball and calculate some of the important degree-based topological indices by using the M-polynomial. We also find the forgotten polynomial and the forgotten index (F-index) for the Buckyball.
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