| Abstract: | We study the resistance distance on connected undirected graphs, linking this concept to the fruitful area of random walks on graphs. We provide two short proofs of a general lower bound for the resistance, or Kirchhoff index, of graphs on N vertices, as well as an upper bound and a general formula to compute it exactly, whose complexity is that of inverting an N×N matrix. We argue that the formulas for the resistance in the case of the Platonic solids can be generalized to all distance‐transitive graphs. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 29–33, 2001 |
