The Hosoya Polynomial of One-Pentagonal Carbon Nanocone

Abstract

Let G be a chemical graph with vertex set V(G) and the distance between vertices u and v in G. The Hosoya polynomial in variable x of graph G is . In this article, we give an analytical expression for calculating the Hosoya polynomial of one-pentagonal carbon nanocone. Furthermore, a series of distance-based molecular structure descriptors, such as the well-known Wiener index, the hyper-Wiener index, and the Harary index, can be easily obtained. From this point of view, we generalize the results on the Wiener index of one-pentagonal carbon nanocone by Ashrafi and Mohammad-Abadi (4).