The Multiplicative Version of the Wiener Index

Journal of Chemical Information and Computer Sciences

Volumn 40, Issue 1, 2000, Pages 113-116

  Gutman, Ivan ^a   Linert, Wolfgang ^b   Lukovits, István ^c   Tomović, Željko ^a  

^a UNIVERSITY OF KRAGUJEVAC   (Serbia)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^c CHEMICAL RESEARCH CENTER   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001472226     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci990060s     Document Type: Article

References (34)

1. Wiener, H. Structural Determination of Paraffin Boiling Points. J. Am. Chem. Soc. 1947, 69, 17-20.
2. For surveys of some of the most frequently encountered topological indexes, see: Balaban, A. T.; Motoc, I.; Bonchev, D.; Mekenyan, O. Topological Indices for Structure-Activity Correlations. Topics Curr. Chem. 1983, 114, 21-55. Seybold, P. G.; May, M.; Bagal, U. A. Molecular Structure-Property Relationships. J. Chem. Educ. 1987, 64, 575-581. Mihalić, Z.; Trinajstić, N. A Graph-Theoretical Approach to Structure-Property Relationships. J. Chem. Educ. 1992, 69, 701-712.
3. For surveys of some of the most frequently encountered topological indexes, see: Balaban, A. T.; Motoc, I.; Bonchev, D.; Mekenyan, O. Topological Indices for Structure-Activity Correlations. Topics Curr. Chem. 1983, 114, 21-55. Seybold, P. G.; May, M.; Bagal, U. A. Molecular Structure-Property Relationships. J. Chem. Educ. 1987, 64, 575-581. Mihalić, Z.; Trinajstić, N. A Graph-Theoretical Approach to Structure-Property Relationships. J. Chem. Educ. 1992, 69, 701-712.
4. For surveys of some of the most frequently encountered topological indexes, see: Balaban, A. T.; Motoc, I.; Bonchev, D.; Mekenyan, O. Topological Indices for Structure-Activity Correlations. Topics Curr. Chem. 1983, 114, 21-55. Seybold, P. G.; May, M.; Bagal, U. A. Molecular Structure-Property Relationships. J. Chem. Educ. 1987, 64, 575-581. Mihalić, Z.; Trinajstić, N. A Graph-Theoretical Approach to Structure-Property Relationships. J. Chem. Educ. 1992, 69, 701-712.
5. Hosoya, H. Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons. Bull. Chem. Soc. Jpn. 1971, 44, 2332-2339.
6. For surveys of the Wiener-type topological indexes and their physicochemical and pharmacological applications, see: Mihalić, Z.; Veljan, D.; Amić, D.; Nikolić, S.; Plavšić, D.; Trinajstić, N. The Distance Matrix in Chemistry. J. Math. Chem. 1992, 11, 223-258. Mihalić, Z.; Nikolić, S.; Trinajstić, N. Comparative Study of Molecular Descriptors Derived from the Distance Matrix. J. Chem. Inf. Comput. Sci. 1992, 32, 28-36. Gutman, I.; Yeh, Y. N.; Lee, S. L.; Luo, Y. L. Some Recent Results in the Theory of the Wiener Number. Indian J. Chem. 1993, 32A, 651-661. Nikolić, S.; Trinajstić, N.; Mihalić, Z. The Wiener Index: Development and Applications. Croat. Chem. Acta 1995, 68, 105-129. Lukovits, I. The Wiener Index and Graph Invariants Derived from It (in Hungarian). Kém. Közlem. 1996, 82, 107-112. Gutman, I.; Potgieter, J. H. Wiener Index and Intermolecular Forces. J. Serb. Chem. Soc. 1997, 62, 185-192. Diudea, M. V.; Gutman, I. Wiener-Type Topological Indices. Croat. Chem. Acta 1998, 71, 21-51.
7. For surveys of the Wiener-type topological indexes and their physicochemical and pharmacological applications, see: Mihalić, Z.; Veljan, D.; Amić, D.; Nikolić, S.; Plavšić, D.; Trinajstić, N. The Distance Matrix in Chemistry. J. Math. Chem. 1992, 11, 223-258. Mihalić, Z.; Nikolić, S.; Trinajstić, N. Comparative Study of Molecular Descriptors Derived from the Distance Matrix. J. Chem. Inf. Comput. Sci. 1992, 32, 28-36. Gutman, I.; Yeh, Y. N.; Lee, S. L.; Luo, Y. L. Some Recent Results in the Theory of the Wiener Number. Indian J. Chem. 1993, 32A, 651-661. Nikolić, S.; Trinajstić, N.; Mihalić, Z. The Wiener Index: Development and Applications. Croat. Chem. Acta 1995, 68, 105-129. Lukovits, I. The Wiener Index and Graph Invariants Derived from It (in Hungarian). Kém. Közlem. 1996, 82, 107-112. Gutman, I.; Potgieter, J. H. Wiener Index and Intermolecular Forces. J. Serb. Chem. Soc. 1997, 62, 185-192. Diudea, M. V.; Gutman, I. Wiener-Type Topological Indices. Croat. Chem. Acta 1998, 71, 21-51.
8. For surveys of the Wiener-type topological indexes and their physicochemical and pharmacological applications, see: Mihalić, Z.; Veljan, D.; Amić, D.; Nikolić, S.; Plavšić, D.; Trinajstić, N. The Distance Matrix in Chemistry. J. Math. Chem. 1992, 11, 223-258. Mihalić, Z.; Nikolić, S.; Trinajstić, N. Comparative Study of Molecular Descriptors Derived from the Distance Matrix. J. Chem. Inf. Comput. Sci. 1992, 32, 28-36. Gutman, I.; Yeh, Y. N.; Lee, S. L.; Luo, Y. L. Some Recent Results in the Theory of the Wiener Number. Indian J. Chem. 1993, 32A, 651-661. Nikolić, S.; Trinajstić, N.; Mihalić, Z. The Wiener Index: Development and Applications. Croat. Chem. Acta 1995, 68, 105-129. Lukovits, I. The Wiener Index and Graph Invariants Derived from It (in Hungarian). Kém. Közlem. 1996, 82, 107-112. Gutman, I.; Potgieter, J. H. Wiener Index and Intermolecular Forces. J. Serb. Chem. Soc. 1997, 62, 185-192. Diudea, M. V.; Gutman, I. Wiener-Type Topological Indices. Croat. Chem. Acta 1998, 71, 21-51.
9. For surveys of the Wiener-type topological indexes and their physicochemical and pharmacological applications, see: Mihalić, Z.; Veljan, D.; Amić, D.; Nikolić, S.; Plavšić, D.; Trinajstić, N. The Distance Matrix in Chemistry. J. Math. Chem. 1992, 11, 223-258. Mihalić, Z.; Nikolić, S.; Trinajstić, N. Comparative Study of Molecular Descriptors Derived from the Distance Matrix. J. Chem. Inf. Comput. Sci. 1992, 32, 28-36. Gutman, I.; Yeh, Y. N.; Lee, S. L.; Luo, Y. L. Some Recent Results in the Theory of the Wiener Number. Indian J. Chem. 1993, 32A, 651-661. Nikolić, S.; Trinajstić, N.; Mihalić, Z. The Wiener Index: Development and Applications. Croat. Chem. Acta 1995, 68, 105-129. Lukovits, I. The Wiener Index and Graph Invariants Derived from It (in Hungarian). Kém. Közlem. 1996, 82, 107-112. Gutman, I.; Potgieter, J. H. Wiener Index and Intermolecular Forces. J. Serb. Chem. Soc. 1997, 62, 185-192. Diudea, M. V.; Gutman, I. Wiener-Type Topological Indices. Croat. Chem. Acta 1998, 71, 21-51.
10. For surveys of the Wiener-type topological indexes and their physicochemical and pharmacological applications, see: Mihalić, Z.; Veljan, D.; Amić, D.; Nikolić, S.; Plavšić, D.; Trinajstić, N. The Distance Matrix in Chemistry. J. Math. Chem. 1992, 11, 223-258. Mihalić, Z.; Nikolić, S.; Trinajstić, N. Comparative Study of Molecular Descriptors Derived from the Distance Matrix. J. Chem. Inf. Comput. Sci. 1992, 32, 28-36. Gutman, I.; Yeh, Y. N.; Lee, S. L.; Luo, Y. L. Some Recent Results in the Theory of the Wiener Number. Indian J. Chem. 1993, 32A, 651-661. Nikolić, S.; Trinajstić, N.; Mihalić, Z. The Wiener Index: Development and Applications. Croat. Chem. Acta 1995, 68, 105-129. Lukovits, I. The Wiener Index and Graph Invariants Derived from It (in Hungarian). Kém. Közlem. 1996, 82, 107-112. Gutman, I.; Potgieter, J. H. Wiener Index and Intermolecular Forces. J. Serb. Chem. Soc. 1997, 62, 185-192. Diudea, M. V.; Gutman, I. Wiener-Type Topological Indices. Croat. Chem. Acta 1998, 71, 21-51.
11. For surveys of the Wiener-type topological indexes and their physicochemical and pharmacological applications, see: Mihalić, Z.; Veljan, D.; Amić, D.; Nikolić, S.; Plavšić, D.; Trinajstić, N. The Distance Matrix in Chemistry. J. Math. Chem. 1992, 11, 223-258. Mihalić, Z.; Nikolić, S.; Trinajstić, N. Comparative Study of Molecular Descriptors Derived from the Distance Matrix. J. Chem. Inf. Comput. Sci. 1992, 32, 28-36. Gutman, I.; Yeh, Y. N.; Lee, S. L.; Luo, Y. L. Some Recent Results in the Theory of the Wiener Number. Indian J. Chem. 1993, 32A, 651-661. Nikolić, S.; Trinajstić, N.; Mihalić, Z. The Wiener Index: Development and Applications. Croat. Chem. Acta 1995, 68, 105-129. Lukovits, I. The Wiener Index and Graph Invariants Derived from It (in Hungarian). Kém. Közlem. 1996, 82, 107-112. Gutman, I.; Potgieter, J. H. Wiener Index and Intermolecular Forces. J. Serb. Chem. Soc. 1997, 62, 185-192. Diudea, M. V.; Gutman, I. Wiener-Type Topological Indices. Croat. Chem. Acta 1998, 71, 21-51.
12. For surveys of the Wiener-type topological indexes and their physicochemical and pharmacological applications, see: Mihalić, Z.; Veljan, D.; Amić, D.; Nikolić, S.; Plavšić, D.; Trinajstić, N. The Distance Matrix in Chemistry. J. Math. Chem. 1992, 11, 223-258. Mihalić, Z.; Nikolić, S.; Trinajstić, N. Comparative Study of Molecular Descriptors Derived from the Distance Matrix. J. Chem. Inf. Comput. Sci. 1992, 32, 28-36. Gutman, I.; Yeh, Y. N.; Lee, S. L.; Luo, Y. L. Some Recent Results in the Theory of the Wiener Number. Indian J. Chem. 1993, 32A, 651-661. Nikolić, S.; Trinajstić, N.; Mihalić, Z. The Wiener Index: Development and Applications. Croat. Chem. Acta 1995, 68, 105-129. Lukovits, I. The Wiener Index and Graph Invariants Derived from It (in Hungarian). Kém. Közlem. 1996, 82, 107-112. Gutman, I.; Potgieter, J. H. Wiener Index and Intermolecular Forces. J. Serb. Chem. Soc. 1997, 62, 185-192. Diudea, M. V.; Gutman, I. Wiener-Type Topological Indices. Croat. Chem. Acta 1998, 71, 21-51.
13. Gutman, I.; Polansky, O. E. Mathematical Concepts in Organic Chemistry; Springer-Verlag: Berlin, 1986.
14. Buckley, F.; Harary, F. Distance in Graphs; Addison-Wesley: Redwood, CA, 1990.
15. Trinajstić, N. Chemical Graph Theory, 2nd ed.; CRC Press: Boca Raton, FL, 1992.
16. Gutman, I.; Vidović, D.; Popović, L. On Graph Representation of Organic Molecules-Cayley's Plerograms vs. His Kenograms. J. Chem. Soc., Faraday Trans. 1998, 94, 857-860.
17. Plavšić, D.; Nikolić, S.; Trinajstić, N.; Mihalić, Z. On the Harary Index for the Characterization of Chemical Graphs. J. Math. Chem. 1993, 12, 235-250.
18. Diudea, M. V. Indices of Reciprocal Properties or Harary Indices. J. Chem. Inf. Comput. Sci. 1997, 37, 292-299. Diudea, M. V.; Ivanciuc, O.; Nikolić, S.; Trinajstić, N. Matrices of Reciprocal Distance, Polynomials and Derived Numbers. Commun. Math. Chem. (MATCH) 1997, 35, 41-64.
19. Diudea, M. V. Indices of Reciprocal Properties or Harary Indices. J. Chem. Inf. Comput. Sci. 1997, 37, 292-299. Diudea, M. V.; Ivanciuc, O.; Nikolić, S.; Trinajstić, N. Matrices of Reciprocal Distance, Polynomials and Derived Numbers. Commun. Math. Chem. (MATCH) 1997, 35, 41-64.
20. Klein, D. J.; Lukovits, I.; Gutman, I. On the Definition of the Hyper-Wiener Index for Cycle-Containing Structures. J. Chem. Inf. Comput. Sci. 1995, 35, 50-52.
21. Tratch, S. S.; Stankevich, M. I.; Zefirov, N. S. Combinatorial Models and Algorithms in Chemistry. The Expanded Wiener Number - A Novel Topological Index. J. Comput. Chem. 1990, 11, 899-908.
22. Klein, D. J.; Gutman, I. Wiener-Number-Related Sequences. J. Chem. Inf. Comput. Sci. 1999, 39, 534-536.
23. Randić, M. Shape Profiles. J. Chem. Inf. Comput. Sci. 1995, 35, 373-382. Randić, M. Molecular Profiles. Novel Geometry-Dependent Molecular Descriptors. New J. Chem. 1995, 19, 781-791. Zhu, H. Y.; Klein, D. J.; Lukovits, I. Extensions of the Wiener Number. J. Chem. Inf. Comput. Sci. 1996, 36, 420-428.
24. Randić, M. Shape Profiles. J. Chem. Inf. Comput. Sci. 1995, 35, 373- 382. Randić, M. Molecular Profiles. Novel Geometry-Dependent Molecular Descriptors. New J. Chem. 1995, 19, 781-791. Zhu, H. Y.; Klein, D. J.; Lukovits, I. Extensions of the Wiener Number. J. Chem. Inf. Comput. Sci. 1996, 36, 420-428.
25. Randić, M. Shape Profiles. J. Chem. Inf. Comput. Sci. 1995, 35, 373- 382. Randić, M. Molecular Profiles. Novel Geometry-Dependent Molecular Descriptors. New J. Chem. 1995, 19, 781-791. Zhu, H. Y.; Klein, D. J.; Lukovits, I. Extensions of the Wiener Number. J. Chem. Inf. Comput. Sci. 1996, 36, 420-428.
26. Gutman, I. Buckley-Type Relations for Wiener-Type Structure-Descriptors J. Serb. Chem. Soc. 1998, 63, 491-496. Gutman, I.; Vidović, D. Relations between Wiener-Type Topological Indices of Plerograms and Kenograms. J. Serb. Chem. Soc. 1998, 63, 695-702.
27. Gutman, I. Buckley-Type Relations for Wiener-Type Structure- Descriptors J. Serb. Chem. Soc. 1998, 63, 491-496. Gutman, I.; Vidović, D. Relations between Wiener-Type Topological Indices of Plerograms and Kenograms. J. Serb. Chem. Soc. 1998, 63, 695-702.
28. To our best knowledge, the only product-form graph invariant every considered in chemical graph theory is Narumi's "simple topological index", equal to the product of vertex degrees: Narumi, H. New Topological Indices for Finite and Infinite Systems. Commun. Math. Chem. (MATCH) 1987, 22, 195-207.
29. Gutman, I.; Linert, W.; Lukovits, I.; Dobrynin, A. A. Trees with Extremal Hyper-Wiener Index: Mathematical Basis and Chemical Applications. J. Chem. Inf. Comput. Sci. 1997, 37, 349-354.
30. Lepovic̀, M.; Gutman, I. A Collective Property of Trees and Chemical Trees. J. Chem. Inf. Comput. Sci. 1998, 38, 823-826.
31. Kirk-Othmer. Encyclopedia of Chemical Technology; Wiley: New York, 1994; Vol. 12 (4); p 348.
32. CD Römpp-Chemielexikon, 9th ed.; Jürgen, F., Ed.; Georg Thieme Verlag: New York, 1995; p 310.
33. Balaban, A. T.; Motoc, I. Chemical Graphs XXXVI. Correlations between Octane Numbers and Topological Indices in Alkanes. Commun. Math. Chem. (MATCH) 1979, 5, 197-218.
34. Balaban, A. T.; Kier, L. B.; Joshi, N. Structure-Property Analysis of Octane Numbers for Hydrocarbons (Alkanes, Cycloalkanes, Alkenes). Commun. Math. Chem. (MATCH) 1992, 28, 13-27.