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
收藏
页码：255 / 263
页数：9
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