Skip to main content

On Some Applications of Information Indices in Chemical Graph Theory

  • Chapter
Book cover General Theory of Information Transfer and Combinatorics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4123))

Abstract

Information theory has been used in various branches of science. During recent years it is applied extensively in chemical graph theory for describing chemical structures and for providing good correlations between physico–chemical and structural properties by means of information indices. The application of information indices to the problem of characterizing molecular structures is presented in the paper. The information indices based on the distance in a graph are considered with respect to their correlating ability and discriminating power.

Mathematics Subject Classification 2000: 94A15, 94A17, 94C15.

This work was partially supported by the RFBR grant 06-01-00694.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Trinajstić, N.: Chemical Graph Theory, 2nd revised edn. CRC Press, Boca Raton (1992)

    Google Scholar 

  2. Rouvray, D.H.: The limits of applicability of topological indices. J. Mol. Struc (Theochem.) 185, 187–201 (1989)

    Article  Google Scholar 

  3. Shannon, C., Weaver, W.: Mathematical Theory of Communications, University of Illinois, Urbana (1949)

    Google Scholar 

  4. Ashby, W.R.: An Introduction to Cybernetics. Wiley, New York (1956)

    MATH  Google Scholar 

  5. Brillouin, L.: Science and Information Theory. Academic, New York (1956)

    MATH  Google Scholar 

  6. Kolmogorov, A.N.: On logic basis of information theory. Probl. Peredachi Inf. 5, 3–7 (1996)

    Google Scholar 

  7. Mowshovitz, A.: The information content of digraphs and infinite graphs. Bull. Math. Biophys. 30, 225–240 (1968)

    Article  MathSciNet  Google Scholar 

  8. Mowshovitz, A.: An index of the relative complexity of a graph. Bull. Math. Biophys. 30, 175–204 (1968)

    Article  MathSciNet  Google Scholar 

  9. Mowshovitz, A.: Graphs with prescribed information content. Bull. Math. Biophys. 30, 387–414 (1968)

    Article  MathSciNet  Google Scholar 

  10. Mowshovitz, A.: Entropy measures and graphical structure. Bull. Math. Biophys. 30, 533–546 (1968)

    Article  MathSciNet  Google Scholar 

  11. Rashevsky, N.: Life, information theory and topology. Bull. Math. Biophys. 17, 229–235 (1955)

    Article  MathSciNet  Google Scholar 

  12. Trucco, E.: A note of the information content of graphs. Bull. Math. Biophys. 17, 129–135 (1956)

    Article  MathSciNet  Google Scholar 

  13. Trucco, E.: On the informational content of graphs–compound symbols, different states for each point. Bull. Math. Biophys. 18, 237–245 (1956)

    Article  MathSciNet  Google Scholar 

  14. Rashevsky, N.: Life, information theory, probability and physics. Bull. Math. Biophys. 22, 351–364 (1960)

    Article  MathSciNet  Google Scholar 

  15. Morovitz, H.: Some order–disorder considerations in living systems. Bull. Math. Biophys. 17, 81–86 (1955)

    Article  Google Scholar 

  16. Valentinuzzi, M., Valentinuzzi, M.E.: Information content of chemical structures and some possible biological applications. Bull. Math. Biophys. 25, 11–27 (1963)

    Article  Google Scholar 

  17. Bonchev, D., Kamenski, D., Kamenska, V.: Symmetry and information content of chemical structures. Bull. Math. Biophys. 38, 119–133 (1976)

    Google Scholar 

  18. Bernstein, R.B., Levine, R.D.: Entropy and chem. change I: characterization of product (and reactant) energy distributions in reactive molecular collisions: information and entropy deficiency. J. Chem. Phys. 57, 434–449 (1972)

    Article  Google Scholar 

  19. Ben-Shaul, A., Levine, R.D., Bernstein, R.B.: Entropy and chem. change II: analysis of product energy distributions: temperature and entropy deficiency. J. Chem. Phys. 57, 5427–5447 (1972)

    Article  Google Scholar 

  20. Aslangul, C., Constanciel, R., Daudel, R., Kottis, P.: Aspects of the localizability of electrons in atoms and molecules: Loge theory and related methods. Adv. Quantum Chem. 6, 93–141 (1972)

    Article  Google Scholar 

  21. Daudel, R., Bader, R.F., Stephens, M.E., Borett, D.S.: The electron pair in chemistry. Can. J. Chem. 52, 1310–1320 (1974)

    Article  Google Scholar 

  22. Aslangul, C., Constanciel, R., Daudel, R., Esnault, L., Ludena, E.: The Loge theory as a starting point for variational calculations, I. General formalism. Int. J. Quantum Chem. 8, 499–522 (1974)

    Article  Google Scholar 

  23. Fratev, F., Enchev, V., Polansky, O.E., Bonchev, D.: A theoretical–information study on the electron delocalization (aromaticity) of annulenes with and without bond alternation. THEOCHEM 88, 105–118 (1982)

    Article  Google Scholar 

  24. Bonchev, D.: Information indices for atoms and molecules. MATCH 7, 65–113 (1979)

    Google Scholar 

  25. Bonchev, D.: Information theory interpretation of the Pauli principle and Hund rule. Intern. J. Quantum Chem. 19, 673–679 (1981)

    Article  Google Scholar 

  26. Wiener, H.: Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69, 17–20 (1947)

    Article  Google Scholar 

  27. Wiener, H.: Vapor pressure–temperature relationships among the branched paraffin hydrocarbons. J. Chem. Phys. 52, 425–430 (1948)

    Article  Google Scholar 

  28. Hosoya, H.: Topological index, a newly proposed quantity characterizing the topological nature of structural isomers of hydrocarbons. Bull. Chem. Soc. Jpn. 44, 2332–2339 (1971)

    Article  Google Scholar 

  29. Randić, M.: On characterization of molecular branching. J. Am. Chem. Soc. 69, 6609–6615 (1975)

    Article  Google Scholar 

  30. Entringer, R.C., Jackson, D.E., Snyder, D.A.: Distance in graphs. Czechoslovak Math.J. 2, 283–297 (1976)

    MathSciNet  Google Scholar 

  31. Doyle, J.K., Graver, J.E.: Mean distance in graphs. Discrete Math. 17, 147–154 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  32. Kier, L.B., Hall, L.H.: Derivation and significance of valence molecular connectivity. J. Pharm. Sci. 70, 583–589 (1981)

    Article  Google Scholar 

  33. Balaban, A.T.: Topological indices based on topological distances in molecular graphs. Pure Appl. Chem. 55, 199–206 (1983)

    Article  Google Scholar 

  34. Rouvray, D.H.: Should we have designs on topological indices? chemical applications of topology and graph theory. In: King, R.B. (ed.) Studies in Physical and Theoretical Chemistry, vol. 28, Elsevier, Amsterdam (1983)

    Google Scholar 

  35. Randić, M.: On molecular identification numbers. J. Chem. Inf. Comput. Sci. 24, 164–175 (1984)

    Google Scholar 

  36. King, R.B., Rouvray, D.H. (eds.): Graph Theory and Topology in Chemistry. Elsevier, Amsterdam (1987)

    MATH  Google Scholar 

  37. Randić, M.: Generalized molecular descriptors. J. Math. Chem. 7, 155–168 (1991)

    Article  Google Scholar 

  38. Nikolić, S., Trinajstić, N., Mihalić, Z.: The Wiener index: developments and applications. Croat. Chem. Acta 68, 105–129 (1995)

    Google Scholar 

  39. Entringer, R.C.: Distance in graphs: trees. J. Combin. Math. Combin. Comput. 24, 65–84 (1997)

    MATH  MathSciNet  Google Scholar 

  40. Diudea, M.V., Gutman, I.: Wiener-type topological indices. Croat. Chem. Acta. 71, 21–51 (1998)

    Google Scholar 

  41. Bonchev, D., Trinajstić, N.: Information theory, distance matrix, and molecular branching. J. Chem. Phys. 38, 4517–4533 (1977)

    Article  Google Scholar 

  42. Bonchev, D., Trinajstić, N.: On topological characterization of molecular branching. Int. J. Quantum Chem. S12, 293–303 (1978)

    Google Scholar 

  43. Bonchev, D., Knop, J.V., Trinajstić, N.: Mathematical models of branching. MATCH 6, 21–47 (1979)

    Google Scholar 

  44. Bonchev, D., Mekenyan, O., Trinajstić, N.: Topological characterization of cyclic structure. Int. J. Quantum Chem. 17, 845–893 (1980)

    Article  Google Scholar 

  45. Bonchev, D., Mekenyan, O., Trinajstić, N.: Isomer discrimination by topological information approach. J. Comput. Chem. 2, 127–148 (1981)

    Article  MathSciNet  Google Scholar 

  46. Bonchev, D., Trinajstić, N.: Chemical information theory, structural aspects. Intern. J. Quantum Chem. Symp. 16, 463–480 (1982)

    Google Scholar 

  47. Bonchev, D.: Information-Theoretic Indices for Characterization of Chemical Structures. Research Studies Press, Chichester (1983)

    Google Scholar 

  48. Kier, L.B., Hall, L.H.: Molecular Connectivity in Chemistry and Drug Research. Academic Press, New York (1976)

    Google Scholar 

  49. Kier, L.B., Hall, L.H.: Molecular Connectivity in Structure–Activity Analysis. Research Studies Press, Letchworth (1986)

    Google Scholar 

  50. Balaban, A.T., Chirac, A., Motoc, I., Simon, Z.: Steric Fit in Quantitative Structure–Activity Relationships. Lecture Notes in Chemistry, vol. 15. Springer, Berlin (1980)

    Google Scholar 

  51. Konstantinova, E.V., Paleev, A.A.: Sensitivity of topological indices of polycyclic graphs (Russian). Vychisl. Sistemy 136, 38–48 (1990)

    MATH  MathSciNet  Google Scholar 

  52. Konstantinova, E.V.: The discrimination ability of some topological and information distance indices for graphs of unbranched hexagonal systems. J. Chem. Inf. Comput. Sci. 36, 54–57 (1996)

    Google Scholar 

  53. Konstantinova, E.V., Diudea, M.V.: The Wiener polynomial derivatives and other topological indices in chemical research. Croat. Chem. Acta 73, 383–403 (2000)

    Google Scholar 

  54. Skorobogatov, V.A., Konstantinova, E.V., Nekrasov, Y.S., Sukharev, Y.N., Tepfer, E.E.: On the correlation between the molecular information topological and mass-spectra indices of organometallic compounds. MATCH 26, 215–228 (1991)

    Google Scholar 

  55. Sukharev, Y.N., Nekrasov, Y.S., Molgacheva, N.S., Tepfer, E.E.: Computer processing and interpretation of mass–spectral information. Part IX - Generalized characteristics of mass–spectra, Org. Mass Spectrom. 28, 1555–1561 (1993)

    Google Scholar 

  56. Yu., S., Nekrasov, E.E., Sukharev, Y.N.: On the relationship between the mass–spactral and structural indices of arylsilanes. Russ. Chem. Bull. 42, 343–346 (1993)

    Article  Google Scholar 

  57. Yu., S., Nekrasov, Y.N., Sukharev, N.S., Tepfer, E.E.: Generalized characteristics of mass–spectra of aromatic compounds and their correlation with the constants of substituents. Russ. Chem. Bull. 42, 1986–1990 (1993)

    Article  Google Scholar 

  58. Nekrasov, Y.S., Sukharev, Y.N., Tepfer, E.E., Molgacheva, N.S.: Establishment of correlations between the structure and reactivity of molecules in the gas phase based on information theory. Russ. Chem. Bull. 45, 2542–2546 (1996)

    Article  Google Scholar 

  59. D’yachkov, A.G., Konstantinova, E.V., Vilenkin, P.A.: On entropy and information of trees, in progress

    Google Scholar 

  60. Konstantinova, E.V., Vidyuk, M.V.: Discriminating tests of information and topological indices, animals and trees. J. Chem. Inf. Comput. Sci. 43(6), 1860–1871 (2003)

    Google Scholar 

  61. Razinger, M., Chretien, J.R., Dubois, J.K.: Structural selectivity of topological indices in alkane series. J. Chem. Inf. Comput. Sci. 25, 23–27 (1985)

    Google Scholar 

  62. Raychaudhary, C., Ray, S.K., Ghosh, J.J., Roy, A.B., Basak, S.C.: Discrimination of isomeric structures using information theoretic topological indices. J. Comput. Chem. 5, 581–588 (1984)

    Article  Google Scholar 

  63. Gutman, I.: Selected properties of the Schultz molecular index. J. Chem. Inf. Comput. Sci. 34, 1087–1089 (1994)

    Google Scholar 

  64. Dobrynin, A.A.: Discriminating power of the Schultz index for cata–condensed benzenoid graphs. MATCH 38, 19–32 (1998)

    MathSciNet  MATH  Google Scholar 

  65. Gutman, I., Cyvin, S.J.: Introduction to the Theory of Benzenoid Hydrocarbons. Springer, Berlin (1989)

    Google Scholar 

  66. Gutman, I., Cyvin, S.J. (eds.): Advances in the Theory of Benzenoid Hydrocarbons. Springer, Berlin (1990)

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Konstantinova, E.V. (2006). On Some Applications of Information Indices in Chemical Graph Theory. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_53

Download citation

  • DOI: https://doi.org/10.1007/11889342_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46244-6

  • Online ISBN: 978-3-540-46245-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics