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Kirchhoff indexes of a network

Author
Bendito, E.; Carmona, A.; Encinas, A.; Gesto, J.; Mitjana, M.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2010-04-15
Volume
432
Number
9
First page
2278
Last page
2292
DOI
https://doi.org/10.1016/j.laa.2009.05.032 Open in new window
Repository
http://hdl.handle.net/2117/8290 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S0024379509002924 Open in new window
Abstract
In this work we define the effective resistance between any pair of vertices with respect to a value λ ≥ 0 and a weight ω on the vertex set. This allows us to consider a generalization of the Kirchhoff Index of a finite network. It turns out that λ is the lowest eigenvalue of a suitable semi-definite positive Schrödinger operator and ω is the associated eigenfunction. We obtain the relation between the effective resistance, and hence between the Kirchhoff Index, with respect to λ and ω ...
Citation
Bendito, E. [et al.]. Kirchhoff indexes of a network. "Linear algebra and its applications", 15 Abril 2010, vol. 432, núm. 9, p. 2278-2292.
Group of research
MAPTHE - Matrix Analysis and Discrete Potential Theory
VARIDIS - Discrete Riemannian Manifolds and Potential Theory

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