Hosoya polynomial of zigzag polyhex nanotorus

Abstract

The Hosoya polynomial of a molecular graph G is defined as ... , where d(u,v) is the distance between vertices u and v. The first derivative of H(G,l) at l = 1 is equal to the Wiener index of G, defined as .... . The second derivative of .... at l = 1 is equal to the hyper-Wiener index, defined as .... . Xu et al. computed the Hosoya polynomial of zigzag open-ended nanotubes. Also Xu and Zhang computed the Hosoya polynomial of armchair open-ended nanotubes. In this paper, a new method was implemented to find the Hosoya polynomial of G = HC6[p,q], the zigzag polyhex nanotori and to calculate the Wiener and hyper Wiener indices of G using H(G,l).

Keywords

• Wiener index
• hyper-Wiener index
• Hosoya polynomial
• nanotubes