About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 305164, 6 pages
http://dx.doi.org/10.1155/2014/305164
Research Article

Energy Conditions for Hamiltonicity of Graphs

1School of Mathematics & Computation Sciences, Anqing Normal College, Anqing 246011, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
3Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 25 December 2013; Accepted 22 January 2014; Published 6 March 2014

Academic Editor: Wenwu Yu

Copyright © 2014 Guidong Yu et al. 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. M. Fiedler and V. Nikiforov, “Spectral radius and Hamiltonicity of graphs,” Linear Algebra and Its Applications, vol. 432, no. 9, pp. 2170–2173, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. Zhou, “Signless Laplacian spectral radius and Hamiltonicity,” Linear Algebra and Its Applications, vol. 432, no. 2-3, pp. 566–570, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. R. Li, “Energy and some Hamiltonian properties of graphs,” Applied Mathematical Sciences, vol. 3, no. 53–56, pp. 2775–2780, 2009. View at Zentralblatt MATH · View at MathSciNet
  4. M. Lu, H. Q. Liu, and F. Tian, “Spectral radius and Hamiltonian graphs,” Linear Algebra and Its Applications, vol. 437, no. 7, pp. 1670–1674, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. Butler and F. Chung, “Small spectral gap in the combinatorial Laplacian implies Hamiltonian,” Annals of Combinatorics, vol. 13, no. 4, pp. 403–412, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Y. Z. Fan and G. D. Yu, “Spectral condition for a graph to be Hamiltonian with respect to normalized Laplacian,” http://arxiv.org/abs/1207.6824.
  7. O. Ore, “Note on Hamilton circuits,” The American Mathematical Monthly, vol. 67, no. 1, p. 55, 1960. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. P. Erdős and T. Gallai, “On maximal paths and circuits of graphs,” Acta Mathematica Academiae Scientiarum Hungaricae, vol. 10, no. 3-4, pp. 337–356, 1959. View at Zentralblatt MATH · View at MathSciNet
  9. A. Bondy and V. Chvátal, “A method in graph theory,” Discrete Mathematics, vol. 15, no. 2, pp. 111–135, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. G. Hendry, “Extending cycles in bipartite graphs,” Journal of Combinatorial Theory B, vol. 51, no. 2, pp. 292–313, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Day and W. So, “Singular value inequality and graph energy change,” Electronic Journal of Linear Algebra, vol. 16, pp. 291–299, 2007. View at Zentralblatt MATH · View at MathSciNet
  12. W. So, “Commutativity and spectra of Hermitian matrices,” Linear Algebra and Its Applications, vol. 212-213, no. 15, pp. 121–129, 1994. View at Scopus