Skip to main content
Log in

Rectifying a misbelief: Frank Harary's role in the discovery of the coefficient-theorem in chemical graph theory

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

It is shown that the formula relating the coefficients of the characteristic polynomial of a graphG to certain structural features ofG (which in mathematical chemistry is traditionally referred to as the Sachs theorem) is a straightforward and relatively easily inferable corollary of an earlier result by Frank Harary.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H. Sachs, Publ. Math. (Debrecen) 11 (1963) 119.

    Google Scholar 

  2. A. Graovac, I. Gutman, N. Trinajstić and T. Živković, Theor. Chim. Acta 26 (1972) 67.

    Google Scholar 

  3. I. Gutman and N. Trinajstić, Topics Curr. Chem. 42 (1973) 49.

    Google Scholar 

  4. D. Cvetković, Publ. Electrotehn. Fak. Beograd, Ser. Mat. Fiz. 354 (1971) 1.

    Google Scholar 

  5. I. Gutman and N. Trinajstić, Croat. Chem. Acta 47 (1975) 527.

    Google Scholar 

  6. N. Trinajstić, Croat. Chem. Acta 49 (1977) 593.

    Google Scholar 

  7. N. Trinajstić,Chemical Graph Theory (CRC Press, Boca Raton,1983, 2nd Ed. 1992).

    Google Scholar 

  8. I. Gutman and O.E. Polansky,Mathematical Concepts in Organic Chemistry (Springer, Berlin, 1986).

    Google Scholar 

  9. I. Gutman, in:Chemical Graph Theory — Introduction and Fundamentals, eds. D. Bonchev and D.H. Rouvray (Gordon and Breach, New York, 1990) pp. 133–176.

    Google Scholar 

  10. J.R. Dias, J. Chem. Educ. 69 (1992) 695.

    Google Scholar 

  11. J.R. Dias,Molecular Orbital Calculations Using Chemical Graph Theory (Springer, Berlin, 1993).

    Google Scholar 

  12. F. Harary, SIAM Rev. 4 (1962) 202.

    Google Scholar 

  13. F. Harary, J. Math. Phys. 38 (1959) 104.

    Google Scholar 

  14. F. Harary,Graph Theory (Addison-Wesley, Reading, 1969) theorems 13.2 and 13.2a.

    Google Scholar 

  15. F. Buckley and F. Harary,Distance in Graphs (Addison-Wesley, Reading, 1990) theorem 6.2.

    Google Scholar 

  16. D. Cvetković, M. Doob and H. Sachs,Spectra of Graphs — Theory and Application (Academic Press, New York, 1980) p. 36.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gutman, I. Rectifying a misbelief: Frank Harary's role in the discovery of the coefficient-theorem in chemical graph theory. J Math Chem 16, 73–78 (1994). https://doi.org/10.1007/BF01169197

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01169197

Keywords

Navigation