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The two-point resistance of a resistor network: a new formulation and application to the cobweb network. (English) Zbl 1285.78003

Summary: We consider the problem of two-point resistance in a resistor network previously studied by the third author [J. Phys. A, Math. Gen. 37, No. 26, 6653–6673 (2004; Zbl 1061.94087)]. By formulating the problem differently, we obtain a new expression for the two-point resistance between two arbitrary nodes which is simpler and can be easier to use in practice. We apply the new formulation to the cobweb resistor network to obtain the resistance between two nodes in the network. Particularly, our results prove a recently proposed conjecture on the resistance between the center node and a node on the network boundary. Our analysis also solves the spanning tree problem on the cobweb network.

MSC:

78A55 Technical applications of optics and electromagnetic theory
94C05 Analytic circuit theory

Citations:

Zbl 1061.94087
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