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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Martina Furrer
Berufsbildungszentrum des Kantons Schaffhausen, 8200 Schaffhausen, Switzerland
Electrical & Electronics Engineering

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Resistors in dual networks Martina Furrer; Norbert Hungerbühler; Simon Jantschgi
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (2020): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2020.8.2.6

Abstract

Let G be a finite plane multigraph and G' its dual. Each edge e of G is interpreted as a resistor of resistance Re, and the dual edge e' is assigned the dual resistance Re':=1/Re. Then the equivalent resistance re over e and the equivalent resistance re' over e' satisfy re/Re+re'/Re'=1. We provide a graph theoretic proof of this relation by expressing the resistances in terms of sums of weights of spanning trees in G and G' respectively.
Co-Authors Norbert Hungerbühler Simon Jantschgi