Graphs and graph polynomials of interest in chemistry

  • Ivan Gutman
Applications In Chemistry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 246)


Various molecular graphs i.e. graphs which represent chemical structures are described. A number of graph polynomials which are of interest in chemical applications are pointed out and some of their properties discussed. Emphasis is given to the computational aspects of the theory of these polynomials.


Chemical Application Characteristic Polynomial Maleic Anhydride Molecular Graph Chemical Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. Balasubramanian, Computer generation of the characteristic polynomial of chemical graphs, J.Comput.Chem. 5 (1984) 387–394.Google Scholar
  2. 2.
    K. Balasubramanian, Characteristic polynomials of organic polymers and periodic structures, J.Comput.Chem. 6 (1985) 656–661.Google Scholar
  3. 3.
    K. Balasubramanian and R. Ramaraj, Computer generation of king and color polynomials of graphs and lattices and their applications to statistical mechanics, J.Comput.Chem. 6 (1985) 447–454.Google Scholar
  4. 4.
    R. Barakat, Characteristic polynomials of chemical graphs via symmetric function theory, Theoret.Chim.Acta 69 (1986) 35–39.CrossRefGoogle Scholar
  5. 5.
    D. Cvetković, M. Doob, I. Gutman and A. Torgašev, Recent Results in the Theory of Graph Spectra, Elsevier, Amsterdam 1986.Google Scholar
  6. 6.
    C.D. Godsil and I. Gutman, On the theory of the matching polynomial, J.Graph Theory 5 (1981) 137–144.Google Scholar
  7. 7.
    C.D. Godsil and I. Gutman, Contribution to the theory of topological resonance energy, Acta Chim.Hung. 110 (1982) 415–424.Google Scholar
  8. 8.
    I. Gutman, Topological properties of benzenoid systems. IX. On the sextet polynomial, Z.Naturforsch. 37a (1982) 69–73.Google Scholar
  9. 9.
    I. Gutman, A. Graovac and B. Mohar, On the existence of a Hermitean matrix whose characteristic polynomial is the matching polynomial of a molecular graph, Math.Chem. 13 (1982) 129–150.Google Scholar
  10. 10.
    I. Gutman and F. Harary, Generalizations of the matching polynomial, Utilitas Math. 24 (1983) 97–106.Google Scholar
  11. 11.
    I. Gutman and O.E. Polansky, Cyclic conjugation and the Hückel molecular orbital model, Theoret.Chim.Acta 60 (1981) 203–226.Google Scholar
  12. 12.
    I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin 1986.Google Scholar
  13. 13.
    A.D.J. Haymet, Footballene: A theoretical prediction for the stable truncated icosahedral molecule C60, J.Amer.Chem.Soc. 108 (1986) 319–321.Google Scholar
  14. 14.
    R.E. Merrifield and H.E. Simmons, The structure of molecular topological spaces, Theoret.Chim.Acta 55 (1980) 55–75.Google Scholar
  15. 15.
    B. Mohar and N. Trinajstić, On computation of the topological resonance energy, J.Comput.Chem. 3 (1982) 28–36.Google Scholar
  16. 16.
    R. Ramaraj and K. Balasubramanian, Computer generation of matching polynomials of chemical graphs and lattices, J.Comput.Chem. 6 (1985) 122–141.Google Scholar
  17. 17.
    M. Randić, On evaluation of the characteristic polynomial for large graphs, J.Comput.Chem. 3 (1982) 421–435.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Ivan Gutman
    • 1
  1. 1.KragujevacYugoslavia

Personalised recommendations