【摘 要】
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We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary, which has not been solved be
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We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary, which has not been solved before, for the Green’s function technique and the Laplacian matrix approach are invalid in this case. Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of finite network. In this paper, we give a general resistance formula which is composed of a single summation, by the recursion-transform method. Meanwhile, several interesting results are derived by the general formula. Further, the current distribution is given explicitly as a byproduct of the method.
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