Random Walks and Foster’s Resistance Theorem

Abstract

Given any simple connected graph G =< V,E > such that each edge e ∈ E has unit resistance, Foster’s Resistance Theorem states that the summation of effective resistances over all edges equals n− 1. That is, ∑ e∈E Re = n− 1 Further, given a general graph with resistances re corresponding to edges e ∈ E, the theorem states: ∑ e∈E Re re = n− 1 Tetali[1] proved… (More)

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