Recursion-Transform method to a non-regular m×n cobweb with an arbitrary longitude

A general Recursion-Transform method is put forward and is applied to resolving a difficult problem of the two-point resistance in a non-regular m × n cobweb network with an arbitrary longitude (or call radial), which has never been solved before as the Green's function technique and the Laplacian matrix approach are difficult in this case. Looking for the explicit solutions of non-regular lattices is important but difficult, since the non-regular condition is like a wall or trap which affects the behavior of finite network. This paper gives several general formulae of the resistance between any two nodes in a non-regular cobweb network in both finite and infinite cases by the R-T method which, is mainly composed of the characteristic roots, is simpler and can be easier to use in practice. As applications, several interesting results are deduced from a general formula, and a globe network is generalized.