Non-commuting graph of the dihedral group determined by Hosoya parameters

Abstract

Hosoya introduced the concept of graph terminologies in chemistry and provide a modeling for molecules. This modeling leads to predict the chemical properties of molecules, easy classification of chemical compounds, computer simulations and computer-assisted design of new chemical compounds. In this article, we determine the non-commuting graph associated with the dihedral group by using three Hosoya parameters (Hosoya polynomial, reciprocal Hosoya polynomial and Hosoya index). These Hosoya parameters contain a pile of information about distance structure as well as the edge independent structure of the above-mentioned graph.