The resistance distance between two vertices of a connected graph is defined as the effective resistance between them in the corresponding electrical network constructed from by replacing each edge of with a unit resistor. The Kirchhoff index of is the sum of resistance distances between all pairs of vertices. In this paper, general bounds for the Kirchhoff index are given via the independence number and the clique number, respectively. Moreover, lower and upper bounds for the Kirchhoff index of planar graphs and fullerene graphs are investigated.
%0 Journal Article
%1 yang14
%A Yang, Yujun
%D 2014
%J Abstract and Applied Analysis
%K circuit effective.resistance eigenvalues graph.theory kirchhoff physics resistor
%P 7
%T Some Bounds for the Kirchhoff Index of Graphs
%U http://dx.doi.org/10.1155/2014/794781
%V 2014
%X The resistance distance between two vertices of a connected graph is defined as the effective resistance between them in the corresponding electrical network constructed from by replacing each edge of with a unit resistor. The Kirchhoff index of is the sum of resistance distances between all pairs of vertices. In this paper, general bounds for the Kirchhoff index are given via the independence number and the clique number, respectively. Moreover, lower and upper bounds for the Kirchhoff index of planar graphs and fullerene graphs are investigated.
@article{yang14,
abstract = {The resistance distance between two vertices of a connected graph is defined as the effective resistance between them in the corresponding electrical network constructed from by replacing each edge of with a unit resistor. The Kirchhoff index of is the sum of resistance distances between all pairs of vertices. In this paper, general bounds for the Kirchhoff index are given via the independence number and the clique number, respectively. Moreover, lower and upper bounds for the Kirchhoff index of planar graphs and fullerene graphs are investigated.},
added-at = {2017-02-15T11:05:06.000+0100},
author = {Yang, Yujun},
biburl = {https://www.bibsonomy.org/bibtex/236284e474ad4eb40bef30fbba82882a9/ytyoun},
description = {Some Bounds for the Kirchhoff Index of Graphs},
interhash = {81a47d0de4473c571709715ae6f357b3},
intrahash = {36284e474ad4eb40bef30fbba82882a9},
journal = {Abstract and Applied Analysis},
keywords = {circuit effective.resistance eigenvalues graph.theory kirchhoff physics resistor},
pages = 7,
timestamp = {2017-04-17T12:16:39.000+0200},
title = {Some Bounds for the {Kirchhoff} Index of Graphs},
url = {http://dx.doi.org/10.1155/2014/794781},
volume = 2014,
year = 2014
}