Resistance between two nodes of a ring network

The resistance between two nodes in some resistor networks has been studied extensively by mathematicians and physicists. Given m positive integers m1,m2,⋯,mn, let G[mi]1n be the resistor network with node set V=V1∪V2∪⋯∪Vn and with a unit resistor between arbitrary two nodes u∈Vi,v∈Vi+1 for i=1,2,⋯,n, where Vi∩Vj=0̸ if i≠j, and ∣Vi∣=mi,Vn+1=V1. Gervacio (2016) introduces a modified method to compute the resistance between two nodes. Based on this method, in this paper, we use the elimination and substitution principles in electrical circuit to obtain the resistance between arbitrary two nodes of G[mi]1n.