Journal of Mathematical Chemistry

, Volume 38, Issue 4, pp 677–684 | Cite as

On the Randić Index of Acyclic Conjugated Molecules

  • Mei Lu
  • Lian-zhu Zhang
  • Feng Tian


The Randić index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))−1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. We give a sharp lower bound on the Randić index of conjugated trees (trees with a perfect matching) in terms of the number of vertices. A sharp lower bound on the Randić index of trees with a given size of matching is also given


Randić index conjugated tree given size of matching 


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  1. 1.
    Randić, M. 1975J. Amer. Chem. Soc976609CrossRefGoogle Scholar
  2. 2.
    Kier, L.B., Hall, L.H. 1976Molecular Connectivity in Chemistry and Drug ResearchAcademic PressSan FranciscoGoogle Scholar
  3. 3.
    Kier L.B., Hall L.H. Molecular Connectivity in Structure-Activity Analysis (Wiley, 1986).Google Scholar
  4. 4.
    Gutman I., Vidović D., Nedić A. J. Serb. Chem. Soc., in press.Google Scholar
  5. 5.
    Gutman, I., Leporić, M. 2001J. Serb. Chem. Soc66605Google Scholar
  6. 6.
    Bollobás, B., Erdös, P. 1998Ars Combin50225Google Scholar
  7. 7.
    Yu, P. 1998J. Math Study (Chinese)31225Google Scholar
  8. 8.
    Hou, Y., Li, J. 2002Linear Algebra Appl342203CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  2. 2.Department of Computer SciencesZhangzhou Teachers CollegeFujianChina
  3. 3.Institute of Systems Science, Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijingChina

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