Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 483735, 8 pages
http://dx.doi.org/10.1155/2014/483735
Research Article

Further Results on the Nullity of Signed Graphs

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received 13 October 2013; Accepted 28 December 2013; Published 18 February 2014

Academic Editor: Qing-Wen Wang

Copyright © 2014 Yu Liu and Lihua You. 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. B. Cheng and B. Liu, “On the nullity of graphs,” Electronic Journal of Linear Algebra, vol. 16, pp. 60–67, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. L. Collatz and U. Sinogowitz, “Spektren endlicher Grafen,” Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 21, pp. 63–77, 1957. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S. C. Gong and G. H. Xu, “On the nullity of a graph with cut-points,” Linear Algebra and Its Applications, vol. 436, no. 1, pp. 135–142, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. I. Gutman and I. Sciriha, “On the nullity of line graphs of trees,” Discrete Mathematics, vol. 232, no. 1–3, pp. 35–45, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. I. Gutman and B. Borovićanin, “Nullity of graphs: an updated survey,” Zbornik Radova, vol. 14(22), pp. 137–154, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. Hu, T. Xuezhong, and B. Liu, “On the nullity of bicyclic graphs,” Linear Algebra and Its Applications, vol. 429, no. 7, pp. 1387–1391, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Li, A. Chang, and W. C. Shiu, “On the nullity of bicyclic graphs,” Match, vol. 60, no. 1, pp. 21–36, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. H. C. Longuert-Higgins, “Resonance structures and MO in unsaturated hydrocarbons,” Journal of Chemical Physics, vol. 18, no. 3, pp. 265–274, 1950. View at Publisher · View at Google Scholar
  9. F. Harary, “On the notion of balance of a signed graph,” The Michigan Mathematical Journal, vol. 2, no. 1, pp. 143–146, 1953. View at Google Scholar · View at MathSciNet
  10. P. J. Cameron, J. J. Seidel, and S. V. Tsaranov, “Signed graphs, root lattices, and Coxeter groups,” Journal of Algebra, vol. 164, no. 1, pp. 173–209, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs, Johann Ambrosius Barth, Heidelberg, Germany, 3rd edition, 1995. View at MathSciNet
  12. B. D. Acharya, “Spectral criterion for cycle balance in networks,” Journal of Graph Theory, vol. 4, no. 1, pp. 1–11, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Z. Fan, Y. Wang, and Y. Wang, “A note on the nullity of unicyclic signed graphs,” Linear Algebra and Its Applications, vol. 438, no. 3, pp. 1193–1200, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Y. Z. Fan, W. X. Du, and C. L. Dong, “The nullity of bicyclic signed graphs,” Linear and Multilinear Algebra, 2013. View at Publisher · View at Google Scholar
  15. I. Gutman, S. L. Lee, J. H. Sheu, and C. Li, “Predicting the nodal properties of molecular orbitals by means of signed graphs,” Bulletin of the Institute of Chemistry, Academia Sinica, vol. 42, pp. 25–32, 1995. View at Google Scholar
  16. Y. P. Hou, J. S. Li, and Y. Pan, “On the Laplacian eigenvalues of signed graphs,” Linear and Multilinear Algebra, vol. 51, no. 1, pp. 21–30, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Y. P. Hou, “Bounds for the least Laplacian eigenvalue of a signed graph,” Acta Mathematica Sinica (English Series), vol. 21, no. 4, pp. 955–960, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. L. Lee and R. R. Lucchese, “Topological analysis of eigenvectors of the adjacency matrices in graph theory: the concept of internal connectivity,” Chemical Physics Letters, vol. 137, no. 3, pp. 279–284, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  19. S. L. Lee and C. Li, “Chemical signed graph theory,” International Journal of Quantum Chemistry, vol. 49, no. 5, pp. 639–648, 1994. View at Publisher · View at Google Scholar
  20. F. S. Roberts, “On balanced signed graphs and consistent marked graphs,” Electronic Notes in Discrete Mathematics, vol. 2, pp. 94–105, 1999. View at Publisher · View at Google Scholar
  21. P. K. Sahu and S. L. Lee, “Net-sign identity information index: a novel approach towards numerical characterization of chemical signed graph theory,” Chemical Physics Letters, vol. 454, no. 1–3, pp. 133–138, 2008. View at Publisher · View at Google Scholar · View at Scopus