Resistances between two nodes of a path network

Abstract

Considerable progress has recently been made in the development of techniques to exactly determine two-point resistances in networks of various topologies. Given n positive integers m1,m2,…,mn, let P[mi]1n be the network with node set V=V1∪V2∪…∪Vn, where Vi∩Vj=∅ if i ≠ j and |Vi|=mi, and with edge set E={uv|u∈Vi,v∈Vi+1,i=1,2,…,n−1}. In this paper, using triangle-star transformation and the principle of substitution, we express arbitrary two nodes resistances of a path network in terms of the number of their nodes.