Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 8, No 2 (2020): Electronic Journal of Graph Theory and Applications

Resistors in dual networks

Martina Furrer (Berufsbildungszentrum des Kantons Schaffhausen, 8200 Schaffhausen, Switzerland)
Norbert Hungerbühler (Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland)
Simon Jantschgi (University of Zurich, 8050 Zurich, Switzerland)

Article Info

Publish Date
16 Oct 2020

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.

Copyrights © 2020




Citation Download
RIS
EndNote, Reference Manager, ProCite
BibTex
Latex, Jabref
Original Source
Download Original
Google Scholar
Check in Google Scholar
Journal Info
Electronic Journal of Graph Theory and Applications (EJGTA)
Website

Abbrev

ejgta

Publisher

Indonesian Combinatorial Society

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...