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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 794781, 7 pages
http://dx.doi.org/10.1155/2014/794781
Research Article

Some Bounds for the Kirchhoff Index of Graphs

School of Mathematics and Information Science, Yantai University, Yantai 264005, China

Received 7 February 2014; Accepted 24 June 2014; Published 10 July 2014

Academic Editor: Massimo Furi

Copyright © 2014 Yujun Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.