Computing the Hosoya Index of Some Nanostar Dendrimers

Abstract

Dendrimers are highly branched macromolecules built up from a monomer, with new branches added in steps until a tree structure is created. The various biological characteristics of dendrimers are a good choice in chemistry, biology, the medical field, and nano-science. A topological index is a type of molecular descriptor that is calculated based on the molecular graph of a chemical structure. The Hosoya index is a well-known topological index that is used to predict some of their physico-chemical properties from the structure of molecules. The Hosoya index of a graph is defined as the total number of its independent edge sets. In this paper, we study the Hosoya index of some families of nanostar dendrimers. We obtain the formulas of the Hosoya index for two infinite classes of dendrimers, namely, nanostar dendrimer  and tetrathiafulvalene dendrimer. We use the Mathematica program to evaluate the results and accuracy of calculations. Our results can be used in analyzing the molecular topology of these families of nanostar dendrimers.