Abstract
The resistance distance r ij between two vertices v i and v j of a (connected, molecular) graph G is equal to the resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any two adjacent points is unity. We show how the matrix elements r ij can be expressed in terms of the Laplacian eigenvalues and eigenvectors of G. In addition, we determine certain properties of the resistance matrix R=||r ij ||.
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Acknowledgements This research was supported by the Natural Science Foundation of China and Fujian Province, and by the Ministry of Sciences, Technologies and Development of Serbia, within Project no. 1389. The authors thank Douglas J. Klein (Galveston) for useful comments.
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Xiao, W., Gutman, I. Resistance distance and Laplacian spectrum. Theor Chem Acc 110, 284–289 (2003). https://doi.org/10.1007/s00214-003-0460-4
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DOI: https://doi.org/10.1007/s00214-003-0460-4