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Effective resistances and Kirchhoff index in subdivision networks

Author
Carmona, A.; Mitjana, M.; Monso, E.
Type of activity
Journal article
Journal
Linear and multilinear algebra
Date of publication
2016-11-12
First page
1
Last page
15
DOI
https://doi.org/10.1080/03081087.2016.1256945 Open in new window
Project funding
The effective resistance as a tool for the study of the inverse problem of the conductances and the analysis of the perturbations on networks
Repository
http://hdl.handle.net/2117/100002 Open in new window
URL
http://www.tandfonline.com/doi/full/10.1080/03081087.2016.1256945 Open in new window
Abstract
We define a subdivision network ¿S of a given network ¿; by inserting a new vertex in every edge, so that each edge is replaced by two new edges with conductances that fulfill electrical conditions on the new network. In this work, we firstly obtain an expression for the Green kernel of the subdivision network in terms of the Green kernel of the base network. Moreover, we also obtain the effective resistance and the Kirchhoff index of the subdivision network in terms of the corresponding param...
Citation
Carmona, A., Mitjana, M., Monso, E. Effective resistances and Kirchhoff index in subdivision networks. "Linear and multilinear algebra", 12 Novembre 2016, p. 1-15.
Keywords
Green kernel, Kirchhoff Index, Resistance distance, Subdivision network
Group of research
MAPTHE - Matrix Analysis and Discrete Potential Theory

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