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Kirchhoff index of linear pentagonal chains
Author(s) -
Wang Yan,
Zhang Wenwen
Publication year - 2009
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.22318
Subject(s) - resistance distance , wiener index , mathematics , hexagonal crystal system , index (typography) , chain (unit) , laplace operator , combinatorics , graph , laplacian matrix , quantum graph , physics , mathematical analysis , quantum mechanics , crystallography , chemistry , computer science , line graph , world wide web , graph power
The resistance distance r ij between two vertices v i and v j of a connected graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf( G ) is the sum of resistance distances between all pairs of vertices. In this article, following the method of Yang and Zhang in the proof of the Kirchhoff index of liner hexagonal chain, we obtain the closed‐form formulae of the Kirchhoff index of liner pentagonal chain P n in terms of its Laplacian spectrum. Finally, we show that the Kirchhoff index of P n is approximately one half of its Wiener index. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010