Advertisement

Journal of Mathematical Chemistry

, Volume 41, Issue 1, pp 45–57 | Cite as

Some upper bounds for the energy of graphs

  • Huiqing Liu
  • Mei Lu
  • Feng Tian
Article

Let G = (V,E) be a graph with n vertices and e edges. Denote V(G) = {v 1,v 2,...,v n }. The 2-degree of v i , denoted by t i , is the sum of degrees of the vertices adjacent to \(v_i, 1\leqslant i\leqslant n\). Let σ i be the sum of the 2-degree of vertices adjacent to v i . In this paper, we present two sharp upper bounds for the energy of G in terms of n, e, t i , and σ i , from which we can get some known results. Also we give a sharp bound for the energy of a forest, from which we can improve some known results for trees.

Keywords

graph energy bipartite forest tree 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Babić D., Gutman I., (1995). MATCH Commun. Math. Comput. 32: 7Google Scholar
  2. 2.
    Cao D.-S., (1998). Linear Algebra Appl. 270: 1CrossRefGoogle Scholar
  3. 3.
    Caporossi G., Cvetković D., Gutman I., Hansen P., (1999). J. Chem. Inf. Comput. Sci. 39: 984CrossRefGoogle Scholar
  4. 4.
    Cvetković D., Doob M., Sachs H., (1980). Spectra of Graphs. Academic Press, New YorkGoogle Scholar
  5. 5.
    Das K.Ch., Kumar P., (2003). Indian J. Pure Appl. Math. 34(6): 149Google Scholar
  6. 6.
    Gutman I., (1974). Chem. Phys. Lett. 24: 283CrossRefGoogle Scholar
  7. 7.
    Gutman I., (1990). J. Chem. Soc. Faraday Trans. 86: 3373CrossRefGoogle Scholar
  8. 8.
    Gutman I., (1992). Topics Curr. Chem. 162: 29CrossRefGoogle Scholar
  9. 9.
    Gutman I., (2001). Algebraic Combinatorics and Applications. Springer-Verlag, Berlin, p. 196.Google Scholar
  10. 10.
    Gutman I., Polansky O.E., (1986). Mathatical Concepts in Organic Chemistry. Springer, BerlinGoogle Scholar
  11. 11.
    Gutman I., Teodorović A.V., Nedeljković L., (1984). Theor. Chim. Acta 65: 23Google Scholar
  12. 12.
    Gutman I., Türker L., Dias J.R., (1986). MATCH Commun. Math. Comput. Chem. 19: 147Google Scholar
  13. 13.
    Koolen J.H., Moulton V., (2001). Adv. Appl. Math. 26: 47CrossRefGoogle Scholar
  14. 14.
    Koolen J.H., Moulton V., (2003). Graphs Comb. 19: 131CrossRefGoogle Scholar
  15. 15.
    Koolen J.H., Moulton V., Gutman I., (2000). Chem. Phys. Lett. 320: 213CrossRefGoogle Scholar
  16. 16.
    McClelland B.J., (1971). J. Chem. Phys. 54: 640CrossRefGoogle Scholar
  17. 17.
    Yu A.M., Lu M., Tian F., (2005). MATCH Commun. Math. Comput. Chem. 53: 441Google Scholar
  18. 18.
    Hong Y., Zhang X.-D., (2005). Dis. Math. 296: 187CrossRefGoogle Scholar
  19. 19.
    Zhou B., (2004). MATCH Commun. Math. Comput. Chem. 51: 111Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceHubei UniversityWuhanChina
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  3. 3.Institute of Systems Science, Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijingChina

Personalised recommendations