Hosoya polynomial of zigzag polyhex nanotorus

Abstract

The Hosoya polynomial of a molecular graph G is defined as H(G,λ)=Σ{u,v}V⊆(G) λd(u,v), where d(u,v) is the distance between vertices u and v. The first derivative of H(G,λ) at λ=1 is equal to the Wiener index of G, defined as W(G)Σ{u,v}⊆V(G)d(u,v). The second derivative of 1/2 λH(G, λ) at λ=1 is equal to the hyper-Wiener index, defined as WW(G)+1/2Σ{u,v}⊆V(G)d(u,v)². Xu et al.1 computed the Hosoya polynomial of zigzag open-ended nanotubes. Also Xu and Zhang2 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,λ).

Keywords

• wiener index
• hyper-wiener index
• hosoya polynomial
• nanotubes