Taiwanese Journal of Mathematics

A Note on the Normalized Laplacian Spectra

Abstract

Let $G$ be a connected graph and $\mathcal{L}$ be its normalized Laplacian matrix. Let $\lambda_1$ be the second smallest eigenvalue of $\mathcal{L}$. In this paper we studied the effect on the second smallest normalized Laplacian eigenvalue by grafting some pendant paths.

Article information

Source
Taiwanese J. Math., Volume 15, Number 1 (2011), 129-139.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406165

Digital Object Identifier
doi:10.11650/twjm/1500406165

Mathematical Reviews number (MathSciNet)
MR2780275

Zentralblatt MATH identifier
1284.05163

Citation

Li, Honghai; Li, Jiongsheng. A Note on the Normalized Laplacian Spectra. Taiwanese J. Math. 15 (2011), no. 1, 129--139. doi:10.11650/twjm/1500406165. https://projecteuclid.org/euclid.twjm/1500406165

References

• A. Banerjee and J. Jost, On the spectrum of the normalzied graph Laplacian, Linear Alg. Appl. 428 (2008), 3015-3022.
• S. Butler, Interlacing for weighted graphs using the normalzied Laplacian, Electronic J. of Linear Alg. 16 (2007), 90-98.
• G. Chen, G. Davis and F. Hall, et. al., An Interlacing Result on Normalized Laplacians, SIAM J. on Discrete Math., 18 (2004), 353-361.
• F. R. K. Chung, Spectral Graph Theory, CBMS. Reg. Conf. Ser. Math. 92, AMS, Providence, RI, 1997.
• M. Fiedler, A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory. Czechoslovak Math. J. 25(100) (1975), 619-633.
• M. Fiedler, Eigenvectors of acyclic matrices. Czechoslovak Math. J. 25(100) (1975), 607-618.
• J. P. Grossman, An eigenvalue bound for the Laplacian of a graph, Discrete Math., 300 (2005), 225-228.
• Jiming Guo, On the Laplacian spectrum of a graph, PhD. Thesis, Department of Applied Mathematics, Tongji University, June 2006.
• S. Kirkland, A note on a distance bound using eigenvalues of the normalized Laplacian matrix, Electronic J. Linear Alg. 16 (2007) 204-207.
• Chi-Kwong Li, A short proof of interlacing inequalities on normalized Laplacians, Linear Alg. Appl., 414 (2006), 425-427.
• H. H. Li, J. S. Li and Y. Z. Fan, The effect on the second smallest eigenvalue of the normalized Laplacian of a graph by grafting edges, Linear and Multilinear Alg., 56 (2008), 627-638.