Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2017, Article ID 2372931, 10 pages
https://doi.org/10.1155/2017/2372931
Research Article

Generalized Characteristic Polynomials of Join Graphs and Their Applications

School of Computer and Communication, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Correspondence should be addressed to Pengli Lu; moc.361@88ilgnepul

Received 11 November 2016; Revised 18 January 2017; Accepted 26 January 2017; Published 2 March 2017

Academic Editor: Francisco R. Villatoro

Copyright © 2017 Pengli Lu 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. D. S. Cvetkovi, M. Doob, and H. Sachs, Spectra of Graphs. Theory and Applications, Johann Ambrosius Barth, Heidelberg, Germany, 3rd edition, 1995. View at MathSciNet
  2. D. J. Klein and M. Randić, “Resistance distance,” Journal of Mathematical Chemistry, vol. 12, no. 1, pp. 81–95, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. I. Gutman and B. Mohar, “The quasi-Wiener and the Kirchhoff indices coincide,” Journal of Chemical Information and Computer Sciences, vol. 36, no. 5, pp. 982–985, 1996. View at Publisher · View at Google Scholar · View at Scopus
  4. R. B. Bapat and S. Gupta, “Resistance distance in wheels and fans,” Indian Journal of Pure and Applied Mathematics, vol. 41, no. 1, pp. 1–13, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. J.-B. Liu, X.-F. Pan, and F.-T. Hu, “The {1}-inverse of the Laplacian of subdivision-vertex and subdivision-edge coronae with applications,” Linear and Multilinear Algebra, vol. 65, no. 1, pp. 178–191, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. Y. Yang, “The Kirchhoff index of subdivisions of graphs,” Discrete Applied Mathematics. The Journal of Combinatorial Algorithms, Informatics and Computational Sciences, vol. 171, pp. 153–157, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. Y. Yang and D. J. Klein, “A recursion formula for resistance distances and its applications,” Discrete Applied Mathematics, vol. 161, no. 16-17, pp. 2702–2715, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Y. Yang and D. J. Klein, “Resistance distance-based graph invariants of subdivisions and triangulations of graphs,” Discrete Applied Mathematics, vol. 181, pp. 260–274, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. Liu and B. Liu, “A Laplacian-energy-like invariant of a graph,” MATCH. Communications in Mathematical and in Computer Chemistry, vol. 59, no. 2, pp. 355–372, 2008. View at Google Scholar · View at MathSciNet
  10. I. Gutman, B. Zhou, and B. Furtula, “The Laplacian-energy like invariant is an energy like invariant,” MATCH. Communications in Mathematical and in Computer Chemistry, vol. 64, no. 1, pp. 85–96, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. B. Arsi, I. Gutman, K. C. Das, and K. Xu, “Relations between Kirchhoff index and Laplacian-energ-like invariant,” Bulletin de l'Académie Serbe des Sciences et des Arts, Classe des Sciences Médicales, vol. 144, pp. 61–72, 2012. View at Google Scholar
  12. K. C. Das, K. Xu, and I. Gutman, “Comparison between Kirchhoff index and the Laplacian-energy-like invariant,” Linear Algebra and Its Applications, vol. 436, no. 9, pp. 3661–3671, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. S.-Y. Cui and G.-X. Tian, “The spectrum and the signless Laplacian spectrum of coronae,” Linear Algebra and Its Applications, vol. 437, no. 7, pp. 1692–1703, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. X. G. Liu, J. Zhou, and C. J. Bu, “Resistance distance and Kirchhoff index of R-vertex join and R-edge join of two graphs,” Discrete Applied Mathematics, vol. 187, pp. 130–139, 2015. View at Google Scholar
  15. X. Liu and S. Zhou, “Spectra of the neighbourhood corona of two graphs,” Linear and Multilinear Algebra, vol. 62, no. 9, pp. 1205–1219, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. C. McLeman and E. McNicholas, “Spectra of coronae,” Linear Algebra and its Applications, vol. 435, no. 5, pp. 998–1007, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. S. Wang and B. Zhou, “The signless Laplacian spectra of the corona and edge corona of two graphs,” Linear and Multilinear Algebra, vol. 61, no. 2, pp. 197–204, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. G. Wilkinson, M. Rosenblum, M. C. Whiting, and R. B. Woodward, “The structure of iron bis-cyclopentadienyl,” Journal of the American Chemical Society, vol. 74, no. 8, pp. 2125–2126, 1952. View at Publisher · View at Google Scholar · View at Scopus
  19. D. M. Cvetkovi, P. Rowlinson, and H. Simi, An Introduction to the Theory of Graph Spectra, Cambridge University Press, Cambridge, UK, 2010.
  20. X. Liu and P. Lu, “Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae,” Linear Algebra and Its Applications, vol. 438, no. 8, pp. 3547–3559, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. X. G. Liu and Z. H. Zhang, “Spectra of subdivision-vertex and subdivision-edge joins of graphs,” https://arxiv.org/abs/1212.0619v3.
  22. F. Z. Zhang, The Schur Complement and Its Applications, Numerical Methods and Algorithms, Springer-Verlag, New York, NY, USA, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  23. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  24. S. Pirzada, H. A. Ganie, and I. Gutman, “On Laplacian energy like invariant and Krichhoff index,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 73, pp. 41–59, 2015. View at Google Scholar