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 m 1 , m 2 , … , m n , let P [ m i ] 1 n be the network with node set V = V 1 ∪ V 2 ∪ … ∪ V n , where V i ∩ V j = ∅ if i ≠ j and | V i | = m i , and with edge set E = { u v | u ∈ V i , v ∈ V i + 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.