Proof and extension of the resistance formula for an m x n cobweb network conjectured by Tan, Zhou and Yang

2013/12/24 by J. W. Essam, J W Essam, Zhi‐Zhong Tan +6 · 1 citation
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Carbon Nanotubes in Composites #FOS: Physical sciences #Graph theory and applications #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Synthesis and Properties of Aromatic Compounds #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1312.6727

7 pages, 3 figures

arxiv created 2013/12/24 · openalex publication_date 2013/12/24 · arxiv updated 2013/12/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

An m x n cobweb network consists of n radial lines emanating from a center and connected by m concentric n-sided polygons. A conjecture of Tan, Zhou and Yang for the resistance from center to perimeter of the cobweb is proved by extending the method used by the above authors to derive formulae for m = 1, 2 and 3 and general n. The resistance of an m x (s+t+1) fan network from the apex to a point on the boundary distant s from the corner is also found.

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• Resistance between two nodes in general position on anm×nfan network

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