Abstract
A novel topological index for the characterization of chemical graphs, derived from the reciprocal distance matrix and named the Harary index in honor of Professor Frank Harary, has been introduced. The Harary index is not a unique molecular descriptor; the smallest pair of the alkane trees with identical Harary indices has been detected in the octane family. The use of the Harary index in the quantitative structure-property relationships is exemplified in modeling physical properties of the C2-C9 alkanes. In this application, the performance of the Harary index is comparable to the performance of the Wiener number.
Similar content being viewed by others
References
J. Dos Passos,The 42nd Parallel (The Modern Library, New York, 1937) p. 325.
N. Trinajstić,Chemical Graph Theory, 2nd. rev. Ed. (CRC, Boca Raton, 1992) ch. 10.
H. Hosoya, Bull. Chem. Soc. Japan 44 (1971)2332.
S.C. Basak, G.J. Niemi and G.D. Veith, in:Computational Chemical Graph Theory, ed. D.H. Rouvray (Nova Science, Commack, New York, 1990) p. 235.
D.H. Rouvray, Sci. Am. 254 (1986)40.
S.V. Nizhnii and N.A. Epshtein, Russian Chem. Rev. 47 (1978)383.
D. Bonchev,Information Theoretic Indices for Characterization of Chemical Structures (Research Studies Press, Chichester, 1983).
H. Hosoya, in:Mathematics and Computational Concepts in Chemistry, ed. N. Trinajstić (Horwood, Chichester, 1986) p. 110.
S.C. Basak, L.J. Monsrud, M.E. Rosen, C.M. Frane and V.R. Magnuson, Acta Pharm. Jugosl. 36 (1986)81.
E. Hladká and L. Matyska, Chemické Listy 82 (1988)1009.
M.I. Stankevitch, I.V. Stankevich and N.S. Zefirov, Russian Chem. Rev. 57 (1988)191.
N. Trinajstić, S. Nikolić and S. Carter, Kern. Ind (Zagreb) 38 (1989)469.
N. Trinajstić, M. Randić and D.J. Klein, Acta Pharm. Jugosl. 36 (1986)267.
L.B. Kier and L.H. Hall,Molecular Connectivity in Chemistry and Drug Research (Academic Press, New York, 1976).
A. Sabljić and N. Trinajstić, Acta Pharm. Jugosl. 31 (1981)71.
L.B. Kier and L.H. Hall,Molecular Connectivity in Structure-Activity Analysis (Research Stu Press, Letchworth, 1986).
P.G. Seybold, M. May and U.A. Bagal, J. Chem. Educ. 64 (1987)575.
A. Sabijić, Environ. Health Perspectives 83 (1989)179.
A. Sabljić, in:Practical Applications of Quantitative Structure-Activity Relationships (QSAR Environmental Chemistry and Toxicology, ed. W. Karcher and J. Devillers (Kluwer, Dordre 1990) p. 61.
O. Ivanciuc, Rev. Roum. Chim. 34 (1989)1361.
T.-S. Balaban, P.A. Filip and O. Ivanciuc, J. Math. Chem. 11 (1992)79.
O. Ivanciuc, T.-S. Balaban and A.T. Balaban, J. Chem. Inf. Comput. Sci., submitted.
H. Wiener, J. Am. Chem. Soc. 69 (1947)17.
D. Bonchev and N. Trinajstić, J. Chem. Phys. 67 (1977)4517.
O.E. Polansky, in:MATH/CHEM/COMP/1988, ed. A. Graovac (Elsevier, Amsterdam, 1989) p.167
Z. Mihalić and N. Trinajstić, J. Chem. Educ. 69 (1992)701.
F. Harary,Graph Theory, 2nd printing (Addison-Wesley, Reading, 1971).
D. Bonchev, A.T. Balaban and O. Mekenyan, J. Chem. Inf. Comput. Sci. 20 (1980)106.
D. Bonchev, A.T. Balaban and M. Randić, Int. J. Quant. Chem. 19 (1981)61; erratum Int. J. Qu Chem. 22(1982)441.
D. Bonchev, O. Mekenyan and A.T. Balaban, J. Chem. Inf. Comput. Sci. 29 (1989)91.
D. Bonchev, J. Mol. Struct. THEOCHEM 185 (1989)155.
D.E. Needham, I.-C. Wei and P.G. Seybold, J. Am. Chem. Soc. 110 (1988)4186.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Frank Harary on the happy occasion of his 70th birthday.
Rights and permissions
About this article
Cite this article
Plavšić, D., Nikolić, S., Trinajstić, N. et al. On the Harary index for the characterization of chemical graphs. J Math Chem 12, 235–250 (1993). https://doi.org/10.1007/BF01164638
Issue Date:
DOI: https://doi.org/10.1007/BF01164638