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

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          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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          Most cited references 3

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          Theory of resistor networks: The two-point resistance

            (2004)
          The resistance between arbitrary two nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulas for two-point resistances are deduced for regular lattices in one, two, and three dimensions under various boundary conditions including that of a Moebius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyze large-size expansions of two-and-higher dimensional lattices.
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            The equivalent resistance of a 3 × n cobweb network and its conjecture of an m × n cobweb network

             Z-Z Tan,  L Zhou,  J.-H. Yang (2013)
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              Resistance and capacitance of 4 × ncobweb network and two conjectures

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                Author and article information

                Journal
                23 December 2013
                Article
                1312.6727

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                7 pages, 3 figures
                cond-mat.stat-mech math-ph math.MP

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