Resistors in dual networks

被引：0

作者：

Furrer, Martina ^{[1
]}

Hungerbuhler, Norbert ^{[2
]}

Jantschgi, Simon ^{[3
]}

机构：

[1] Berufsbildungszentritin Kantons Schaffhausen, CH-8200 Schaffhausen, Switzerland

[2] Swiss Fed Inst Technol, Dept Math, CH-8092 Zurich, Switzerland

[3] Univ Zurich, CH-8050 Zurich, Switzerland

来源：

ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS | 2020年 / 8卷 / 02期

关键词：

dual graphs; electrical networks; equivalent resistance; MINORS;

D O I：

10.5614/ejgta.2020.8.2.6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 R-e' := 1/R-e. Then the equivalent resistance re over e and the equivalent resistance r(e') over e' satisfy r(e)/R-e+r(e')/R-e' = 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.

引用

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页码：255 / 263

页数：9

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