On Molecular Structural Characterization of Cyclen Cored Dendrimers

Abstract

Macromolecules are gaining much attention in various fields today. Dendrimers are artificially synthesized macromolecules by convergent or divergent approach. They are compact regular structures with spherical dimension and has a vast number of application in disparate fields such as drug delivery, material science, and biology, magnetic resonance imaging, an organic light-emitting device, etc. Determining the pharmacological, chemical, and biological characteristics of a substance necessitates a significant amount of effort. From the chemical graph of the dendrimer structure, we can infer those characteristics with the help of numerical descriptors known as the topological index. The Wiener and Szeged indices are two important distance-based topological indices applicable in nanoscience. The degree-based topological indices also have great importance and huge applications in structural chemistry. These indices together with graph entropy are found to be more effective and have found application in different sciences. In this work, the Wiener index, Szeged indices, Mostar indices, and Padmakar Ivan index for cyclen cored dendrimers are evaluated by converting the original graph into quotient graphs using ${\Theta }^{*}$- classes. This technique is applied since the regular cut method is a lengthy process while moving on to higher generations and also due to the presence of odd cycles in the structure. The degree-based indices and the degree-based graph entropies for the cyclen cored dendrimers are further studied. The comparison graphs with respect to the topological indices as well as graph entropies are also presented.

Keywords:

• Distance based index
• degree based index
• graph entropy
• cyclen cored dendrimers

Disclosure statement

No potential conflict of interest was reported by the author(s).