Journal of Mathematical Chemistry

, Volume 41, Issue 1, pp 33–43 | Cite as

The Merrifield–Simmons Indices and Hosoya Indices of Trees with k Pendant Vertices


The Merrifield–Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we characterize the trees with maximal Merrifield–Simmons indices and minimal Hosoya indices, respectively, among the trees with k pendant vertices.


Merrifield–Simmons index Hosoya index tree pendant vertex 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alameddine A.F. (1998). Fibonacci Quart. 36:206Google Scholar
  2. 2.
    Bondy J.A., and Murty U.S.R. (1976). Graph Theory with Applications. Macmillan, New YorkGoogle Scholar
  3. 3.
    Chan O., Gutman I., Lam T.K., and Merris R. (1998). J. Chem. Inform. Comput. Sci 38:62CrossRefGoogle Scholar
  4. 4.
    Cyvin S.J., and Gutman I. (1988). MATCH. Commun. Math. Comput. Chem. 23:89Google Scholar
  5. 5.
    Cyvin S.J., Gutman I., and Kolakovic N. (1989). MATCH Commun. Math. Comput. Chem. 24:105Google Scholar
  6. 6.
    Gutman I. (1988). MATCH Commun. Math. Comput. Chem 23:95Google Scholar
  7. 7.
    Gutman I. (1993). J. Math. Chem 12:197CrossRefGoogle Scholar
  8. 8.
    Gutman I., and Polansky O.E. (1986). Mathematical Concepts in Organic Chemistry. Springer, BerlinGoogle Scholar
  9. 9.
    Gutman I., Vidović D. and Furtula B. (2002). Chem. Phys. Lett 355:378CrossRefGoogle Scholar
  10. 10.
    Hosoya H. (1971). Topological index. Bull. Chem. Soc. Jpn. 44:2332CrossRefGoogle Scholar
  11. 11.
    Hou Y.P. (2002). Discrete Appl. Math 119:251CrossRefGoogle Scholar
  12. 12.
    Li X.L., Zhao H.X., and Gutman I. (2005). MATCH Commun. Math. Comput. Chem 54:389Google Scholar
  13. 13.
    Merrifield R.E., and Simmons H.E. (1989). Topological Methods in Chemistry. Wiley, New YorkGoogle Scholar
  14. 14.
    Pedersen A.S., and Vestergaard P.D. (2005). Discrete Appl. Math 152:246CrossRefGoogle Scholar
  15. 15.
    Prodinger H., and Tichy R.F. (1982). Fibonacci Quart 20:16Google Scholar
  16. 16.
    Türker L. (2003). J. Mol. Struct (Theochem) 623:75CrossRefGoogle Scholar
  17. 17.
    Zhang L.Z. (1998). J. Sys. Sci. Math. Sci 18:460Google Scholar
  18. 18.
    Zhang L.Z., Singly-angular hexagonal chains and Hosoya index, submitted.Google Scholar
  19. 19.
    Zhang L.Z., and Tian F. (2001). Sci. Chn. (Series A) 44:1089Google Scholar
  20. 20.
    Zhang L.Z., and Tian F. (2003). J. Math. Chem 34:111CrossRefGoogle Scholar
  21. 21.
    Yu A.M., and Tian F. (2006). MATCH Commun. Math. Comput. Chem. 55:103Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Jiaotong UniversityBeijingChina
  2. 2.Department of MathematicsRenmin University of ChinaBeijingChina

Personalised recommendations