论文信息 - Lower Bounds for the Kirchhoff Index

Lower Bounds for the Kirchhoff Index

Zhou and Trinajstic in (17) and Das, Gungor, and Cevik in (6) obtained lower bounds for the Kirchhoff index of a connected graph. Using some ideas in (17), (6), and other established results, we obtain new lower bounds for the Kirchhoff index of a connected graph.

Rao Li | Rao Li

[1] Douglas J. Klein,et al. Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances or reciprocal distances , 1994 .

[2] Li Jiong. Note on the Algebraic Connectivity of a Graph , 2002 .

[3] Gordon F. Royle,et al. Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[4] Russell Merris,et al. The Laplacian Spectrum of a Graph II , 1994, SIAM J. Discret. Math..

[5] Kinkar Ch. Das. The largest two Laplacian eigenvalues of a graph , 2004 .

[6] A. Sinan Çevik,et al. On Kirchhoff Index and Resistance-Distance Energy of a Graph , 2012 .

[7] Ji-Ming Guo. On the third largest Laplacian eigenvalue of a graph , 2007 .

[8] Bo Zhou,et al. A note on Kirchhoff index , 2008 .

[9] István Lukovits,et al. Extensions of the Wiener Number , 1996, J. Chem. Inf. Comput. Sci..

[10] Bojan Mohar,et al. The Quasi-Wiener and the Kirchhoff Indices Coincide , 1996, J. Chem. Inf. Comput. Sci..

[11] Steve Kirkland,et al. A bound on the algebraic connectivity of a graph in terms of the number of cutpoints , 2000 .

[12] Hua Bai. The Grone-Merris Conjecture , 2009, 0911.2172.

[13] M. Fiedler. Algebraic connectivity of graphs , 1973 .