Hosoya polynomials of armchair open‐ended nanotubes |
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| Authors: | Shoujun Xu Heping Zhang |
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| Institution: | 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China;2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China |
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| Abstract: | For a connected graph G we denote by d(G,k) the number of vertex pairs at distance k. The Hosoya polynomial of G is H(G,x) = ∑k≥0 d(G,k)xk. In this paper, analytical formulae for calculating the polynomials of armchair open‐ended nanotubes are given. Furthermore, the Wiener index, derived from the first derivative of the Hosoya polynomial in x = 1, and the hyper‐Wiener index, from one‐half of the second derivative of the Hosoya polynomial multiplied by x in x = 1, can be calculated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 |
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| Keywords: | Hosoya polynomial armchair open‐ended nanotube Wiener index hyper‐Wiener index |
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