The Hosoya polynomial of a molecular graph G is defined as H(G,λ) =∑_([u,v]∈V(i))λ~(d(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) = ∑_([u,v]∈V(i))λ~(d(u,v)). The second derivative of 1/2λH(G,λ) at λ = 1 is equal to the hyper-Wiener index, defined as WW(G) =1/2W(G) +1/2∑_([u,v]∈V(i))d(u,v)~2 Xu et al. computed the Hosoya polynomial of zigzag open-~ended nanotubes. Also Xu and Zhang~2 computed the Hosoya polynomial of armchair open-ended nanotubes. In this paper, a new method was implemented to find the Hosoya polynomial of G = HC_6[p,q], the zigzag polyhex nanotori and to calculate the Wiener and hyper Wiener indices of G using H(G, λ).
展开▼
