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Hosoya polynomials of armchair open‐ended nanotubes
Author(s) -
Xu Shoujun,
Zhang Heping
Publication year - 2006
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21161
Subject(s) - wiener index , combinatorics , vertex (graph theory) , polynomial , mathematics , graph , topological index , derivative (finance) , mathematical analysis , financial economics , economics
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 ) x k . 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