Resistors in dual networks
| Main Authors: | Furrer, Martina; Berufsbildungszentrum des Kantons Schaffhausen, 8200 Schaffhausen, Switzerland, Hungerbühler, Norbert; Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland, Jantschgi, Simon; University of Zurich, 8050 Zurich, Switzerland |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2020
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/657 https://www.ejgta.org/index.php/ejgta/article/view/657/pdf_141 |
Daftar Isi:
- 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.