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Ars Combinatoria

  • Research article

A Note on the Kirchhoff Index of Bicyclic Graphs

Lihua Feng1,2, Guihai Yu2, Kexiang Xu3, Zhengtao Jiang4
1Department of Mathematics, Central South University Railway Campus, Changsha, Hunan, 410075, P.R. China.
2School of Mathematics, Shandong Institute of Business and Technology 191 Binhaizhong Road, Yantai, Shandong, 264005, P.R. China.
3College of Science, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, P.R. China
4School of Computer Science, Communication University of China Beijing 100024, P.R. China. e-mail: fenglh0163.com
  • Published: 30/04/2014

Abstract

Resistance distance was introduced by Klein and Randic as a generalization of the classical distance. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all pairs of vertices. In this paper, we determine the bicyclic graph of order n≥8 with maximal Kirchhoff index. This improves and extends an earlier result by Zhang etal.[19].

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