The equivalent resistance of a 3 × n cobweb network and its conjecture of an m × n cobweb network

Abstract

We investigate the equivalent resistance of a 3 × n cobweb network. The difference equations of the model are constructed by network analysis and their general solution is obtained by matrix transformations. It is found that the equivalent resistance can be expressed by the trigonometric function of kπ/7, which decreases with the increase of the order n. By analyzing and comparing the equivalent resistances of the 1 × n, 2 × n and 3 × n cobweb networks, a conjecture on the equivalent resistance of the m × n cobweb network is proposed.