Skip to main content

Advertisement

SpringerLink
Log in

Maximum energy trees with two maximum degree vertices

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The energy E of a graph G is equal to the sum of the absolute values of the eigenvalues of G. In 2005 Lin et al. determined the trees with a given maximum vertex degree Δ and maximum E, that happen to be trees with a single vertex of degree Δ. We now offer a simple proof of this result and, in addition, characterize the maximum energy trees having two vertices of maximum degree Δ.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cvetković D., Doob M., Sachs H.: Spectra of Graphs—Theory and Application. Academic Press, New York (1980)

    Google Scholar 

  2. Gutman I.: Ber. Math.–Statist. Sekt. Forschungsz. Graz 103, 1 (1978)

    Google Scholar 

  3. Gutman I.: J. Math. Chem. 1, 123 (1987)

    CAS  Google Scholar 

  4. Coulson C.A.: Proc. Cambridge Phil. Soc. 36, 201 (1940)

    Article  CAS  Google Scholar 

  5. C.A. Coulson, J. Jacobs, J. Chem. Soc. 2805 (1949)

  6. Hall G.G.: Proc. R. Soc. A 229, 251 (1955)

    Article  CAS  Google Scholar 

  7. Hall G.G.: Trans. Faraday Soc. 53, 573 (1957)

    Article  CAS  Google Scholar 

  8. Ruedenberg K.: J. Chem. Phys. 29, 1232 (1958)

    Article  CAS  Google Scholar 

  9. Ruedenberg K.: J. Chem. Phys. 34, 1884 (1961)

    Article  CAS  Google Scholar 

  10. McClelland B.J.: J. Chem. Phys. 54, 640 (1971)

    Article  CAS  Google Scholar 

  11. Gutman I.: Chem. Phys. Lett. 24, 283 (1974)

    Article  CAS  Google Scholar 

  12. Gutman I.: Theor. Chim. Acta 35, 355 (1974)

    Article  CAS  Google Scholar 

  13. Gutman I.: Theor. Chim. Acta 45, 79 (1977)

    Article  CAS  Google Scholar 

  14. Koolen J., Moulton V.: Adv. Appl. Math. 26, 47 (2001)

    Article  Google Scholar 

  15. Koolen J., Moulton V.: Graph Combin. 19, 131 (2003)

    Article  Google Scholar 

  16. W.H. Haemers, Lin. Algebra Appl. (in press)

  17. Wang M., Hua H., Wang D.: J. Math. Chem. 43, 1389 (2008)

    Article  CAS  Google Scholar 

  18. Yan W., Ye L.: Appl. Math. Lett. 18, 1046 (2005)

    Article  Google Scholar 

  19. Yan W., Ye L.: MATCH Commun. Math. Comput. Chem. 53, 449 (2005)

    CAS  Google Scholar 

  20. Lin W., Guo X., Li H.: MATCH Commun. Math. Comput. Chem. 54, 363 (2005)

    Google Scholar 

  21. Zhou B., Li F.: J. Math. Chem. 39, 465 (2006)

    Article  CAS  Google Scholar 

  22. Yu A., Lv X.: Lin. Algebra Appl. 418, 625 (2006)

    Article  Google Scholar 

  23. Ye L., Yuan X.: MATCH Commun. Math. Comput. Chem. 57, 193 (2007)

    Google Scholar 

  24. Li N., Li S.: MATCH Commun. Math. Comput. Chem. 59, 291 (2008)

    CAS  Google Scholar 

  25. Gutman I., Radenković S., Li N., Li S.: MATCH Commun. Math. Comput. Chem. 59, 315 (2008)

    CAS  Google Scholar 

  26. Ou J.: J. Math. Chem. 43, 328 (2008)

    Article  CAS  Google Scholar 

  27. Li S., Li X.: MATCH Commun. Math. Comput. Chem. 61, 383 (2009)

    Google Scholar 

  28. Hou Y.: J. Math. Chem. 29, 163 (2001)

    Article  CAS  Google Scholar 

  29. Gutman I., Hou Y.: MATCH Commun. Math. Comput. Chem. 43, 17 (2001)

    CAS  Google Scholar 

  30. Hou Y., Gutman I., Woo C.W.: Lin. Algebra Appl. 356, 27 (2002)

    Article  Google Scholar 

  31. Li F., Zhou B.: MATCH Commun. Math. Comput. Chem. 54, 379 (2005)

    Google Scholar 

  32. Wang W.H., Chang A., Zhang L.Z., Lu D.Q.: J. Math. Chem. 39, 231 (2006)

    Article  CAS  Google Scholar 

  33. Hua H.: MATCH Commun. Math. Comput. Chem. 57, 351 (2007)

    Google Scholar 

  34. Hua H.: MATCH Commun. Math. Comput. Chem. 58, 57 (2007)

    Google Scholar 

  35. Gutman I., Furtula B., Hua H.: MATCH Commun. Math. Comput. Chem. 58, 85 (2007)

    Google Scholar 

  36. Hua H., Wang M.: Lin. Algebra Appl. 426, 478 (2007)

    Article  Google Scholar 

  37. Wang W.H., Chang A., Lu D.Q.: J. Math. Chem. 42, 311 (2007)

    Article  CAS  Google Scholar 

  38. Li X., Zhang J., Zhou B.: J. Math. Chem. 42, 729 (2007)

    Article  CAS  Google Scholar 

  39. Li F., Zhou B.: J. Math. Chem. 43, 476 (2008)

    Article  CAS  Google Scholar 

  40. Li S., Li X., Zhu Z.: MATCH Commun. Math. Comput. Chem. 61, 325 (2009)

    CAS  Google Scholar 

  41. Hou Y.: Lin. Multilin. Algebra 49, 347 (2002)

    Article  Google Scholar 

  42. Zhang J., Zhou B.: J. Math. Chem. 37, 423 (2005)

    Article  CAS  Google Scholar 

  43. Li X., Zhang J.: Lin. Algebra Appl. 427, 87 (2007)

    Article  Google Scholar 

  44. Yang Y., Zhou B.: MATCH Commun. Math. Comput. Chem. 59, 321 (2008)

    CAS  Google Scholar 

  45. Liu Z., Zhou B.: MATCH Commun. Math. Comput. Chem. 59, 381 (2008)

    CAS  Google Scholar 

  46. Li S., Li X., Zhu Z.: MATCH Commun. Math. Comput. Chem. 59, 397 (2008)

    Google Scholar 

  47. Zhang F., Li Z., Wang L.: Chem. Phys. Lett. 337, 125 (2001)

    Article  CAS  Google Scholar 

  48. Zhang F., Li Z., Wang L.: Chem. Phys. Lett. 337, 131 (2001)

    Article  CAS  Google Scholar 

  49. Rada J., Tineo A.: Lin. Algebra Appl. 372, 333 (2003)

    Article  Google Scholar 

  50. Ren H., Zhang F.: J. Math. Chem. 42, 1041 (2007)

    Article  CAS  Google Scholar 

  51. I. Gutman, in Algebraic Combinatorics and Applications, ed. by A. Betten, A. Kohnert, R. Laue, A. Wassermann (Springer-Verlag, Berlin, 2001), pp. 196–211

  52. Gutman I., Zhang F.: Discr. Appl. Math. 15, 25 (1986)

    Article  Google Scholar 

  53. Gutman I., Polansky O.E.: Mathematical Concepts in Organic Chemistry. Springer-Verlag, Berlin (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin, 300071, People’s Republic of China

    Xueliang Li, Xiangmei Yao & Jianbin Zhang

  2. Faculty of Science, University of Kragujevac, P.O. Box 60, Kragujevac, 34000, Serbia

    Ivan Gutman

Authors
  1. Xueliang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiangmei Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianbin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ivan Gutman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xueliang Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, X., Yao, X., Zhang, J. et al. Maximum energy trees with two maximum degree vertices. J Math Chem 45, 962–973 (2009). https://doi.org/10.1007/s10910-008-9394-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-008-9394-3

Keywords

Search

Navigation