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A formula for the Kirchhoff index
Author(s) -
Bendito Enrique,
Carmona Angeles,
Encinas Andres M.,
Gesto Jose M.
Publication year - 2008
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.21588
Subject(s) - homogeneous space , index (typography) , mathematics , wiener index , expression (computer science) , kirchhoff integral theorem , mathematical analysis , mathematical physics , combinatorics , geometry , computer science , graph , world wide web , partial differential equation , summation equation , programming language
Abstract We show here that the Kirchhoff index of a network is the average of the Wiener capacities of its vertices. Moreover, we obtain a closed‐form formula for the effective resistance between any pair of vertices when the considered network has some symmetries, which allows us to give the corresponding formulas for the Kirchhoff index. In addition, we find the expression for the Foster's n ‐th formula.