%0 Journal Article %1 palacios01 %A Palacios, José Luis %D 2001 %I John Wiley & Sons, Inc. %J International Journal of Quantum Chemistry %K circuit effective.resistance graph.theory random.walk %N 1 %P 29--33 %R 10.1002/1097-461X(2001)81:1<29::AID-QUA6>3.0.CO;2-Y %T Resistance Distance in Graphs and Random Walks %V 81 %X 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

@article{palacios01, 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}, added-at = {2017-02-01T08:05:24.000+0100}, author = {Palacios, Jos\'{e} Luis}, biburl = {https://www.bibsonomy.org/bibtex/2afa2ceca7ce682e022a6282e38763cdd/ytyoun}, description = {Resistance distance in graphs and random walks - Palacios - 2000 - International Journal of Quantum Chemistry - Wiley Online Library}, doi = {10.1002/1097-461X(2001)81:1<29::AID-QUA6>3.0.CO;2-Y}, interhash = {b127392d6c4ec39ee7044a16af2b1641}, intrahash = {afa2ceca7ce682e022a6282e38763cdd}, issn = {1097-461X}, journal = {International Journal of Quantum Chemistry}, keywords = {circuit effective.resistance graph.theory random.walk}, number = 1, pages = {29--33}, publisher = {John Wiley & Sons, Inc.}, timestamp = {2017-02-04T10:29:49.000+0100}, title = {Resistance Distance in Graphs and Random Walks}, volume = 81, year = 2001 }