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The Kirchhoff index and the matching number
Author(s) -
Zhou Bo,
Trinajstić Nenad
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.21915
Subject(s) - wiener index , resistance distance , eigenvalues and eigenvectors , mathematics , topological index , matching (statistics) , index (typography) , combinatorics , quantum graph , graph , laplacian matrix , connectivity , quantum , laplace operator , physics , quantum mechanics , mathematical analysis , line graph , computer science , statistics , graph power , world wide web
The Kirchhoff index of a connected (molecular) graph is the sum of the resistance‐distances between all unordered pairs of vertices and may also be expressed by its Laplacian eigenvalues. We determine the minimum Kirchhoff index of connected (molecular) graphs in terms of the number of vertices and matching number and characterize the unique extremal graph. The results on the Kirchhoff index are compared with the corresponding results on the Wiener index. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009