Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 720854, 4 pages
http://dx.doi.org/10.1155/2013/720854
Research Article

Sharp Upper Bounds for the Laplacian Spectral Radius of Graphs

1Department of Mathematics, Shaoyang University, Hunan 422000, China
2Shaoyang Radio & TV University, Hunan 422000, China

Received 15 August 2013; Accepted 10 October 2013

Academic Editor: Miguel A. F. Sanjuán

Copyright © 2013 Houqing Zhou and Youzhuan Xu. 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.

Linked References

  1. L. M. Pecora and T. L. Carroll, “Master stability functions for synchronized coupled systems,” Physical Review Letters, vol. 80, no. 10, pp. 2109–2112, 1998. View at Google Scholar · View at Scopus
  2. F. Dorfler and F. Bullo, “Synchronization and transient stability in power networks and non-uniform kuramoto oscillators,” SIAM Journal on Control and Optimization, vol. 50, pp. 1616–1642, 2012. View at Publisher · View at Google Scholar
  3. R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi-agent systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 215–233, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. R. Merris, “Laplacian matrices of graphs: a survey,” Linear Algebra and Its Applications, vol. 197-198, pp. 143–176, 1994. View at Google Scholar · View at Scopus
  5. L. Shi, “Bounds on the (Laplacian) spectral radius of graphs,” Linear Algebra and Its Applications, vol. 422, no. 2-3, pp. 755–770, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Li, W. C. Shiu, and A. Chang, “The Laplacian spectral radius of graphs,” Czechoslovak Mathematical Journal, vol. 60, no. 3, pp. 835–847, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Dyilek Maden and S. Buyukkose, “Bounds for Laplacian graph eigenvalues,” Mathematical Inequalities & Applications, vol. 12, pp. 529–536, 2012. View at Google Scholar
  8. S. M. Cioabǎ, “Sums of powers of the degrees of a graph,” Discrete Mathematics, vol. 306, no. 16, pp. 1959–1964, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. M. N. Ellingham and X. Zha, “The spectral radius of graphs on surfaces,” Journal of Combinatorial Theory B, vol. 78, no. 1, pp. 45–56, 2000. View at Publisher · View at Google Scholar · View at Scopus
  10. J. Shu, Y. Hong, and R. Wen, “A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph,” Linear Algebra and Its Applications, vol. 347, no. 1–3, pp. 123–129, 2002. View at Publisher · View at Google Scholar