Abstract
AbstractWe give an elementary proof of an extension of Broder and Karlin's formula for the hitting times of an arbitrary ergodic Markov chain. Using this formula in the particular case of random walks on graphs, we give upper and tight lower bounds for the Kirchhoff index of any N‐ vertex graph in terms of N and its maximal and minimal degrees. We also apply the formula to a closely related index that takes into account the degrees of the vertices between which the effective resistances are computed. We give an upper bound for this alternative index and show that the bound is attained—up to a constant—for the barbell graph. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.