Modeling Boiling Points of Cycloalkanes by Means of Iterated Line Graph Sequences

Journal of Chemical Information and Computer Sciences

Volumn 41, Issue 4, 2001, Pages 1041-1045

  Tomović, Željko ^a   Gutman, Ivan ^a  

^a UNIVERSITY OF KRAGUJEVAC   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE;

BOILING POINTS;

APPROXIMATION THEORY; ATOMS; CARBON; COMPUTER SIMULATION; GRAPH THEORY; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; MOLECULAR GRAPHICS; MOLECULAR STRUCTURE;

PARAFFINS;

EID: 0035412797     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci010006n     Document Type: Article

References (37)

1. Mihalić, Z.; Trinajstić, N. A Graph-Theoretical Approach to Structure-Property Relationships. J. Chem. Educ. 1992, 69, 701-712.
2. Das, A.; Dömötör. G.; Gutman, I.; Joshi, S.; Karmarkar, S.; Khaddar, D.; Khaddar, T.; Khadikar, P. V.; Popović, L.; Sapre, N. S.; Sapre, N.; Shirhatti, A. A Comparative Study of the Wiener, Schultz and Szeged Indices of Cycloalkanes, J. Serb. Chem. Soc. 1997, 62, 235- 239.
3. Rücker, G.; Rücker, C. On Topological Indices, Boiling Points, and Cycloalkanes. J. Chem. Inf. Comput. Sci. 1999, 39, 788-802.
4. Benz, S. H. The Bond Graph. J. Chem. Soc. Chem. Commun. 1981, 818-820.
5. 25 it escaped the attention of the majority of scientists working in chemical graph theory.
6. Platt, J. R. Influence of Neighbour Bonds on Additive Bond Properties in Paraffins. J. Chem. Phys. 1947, 15, 419-420.
7. Platt, J. R. Prediction of Isomeric Differences in Paraffin Properties. J. Phys. Chem. 1952, 56, 328-336.
8. Gutman, I. Topological Properties of Benzenoid Systems. IX. On the Sextet Polynomial. Z. Naturforsch. 1982, 37a, 69-73.
9. Sana, M.; Leroy, G. Graph Theory, Electronic Structures and Reaction Mechanisms. J. Mol. Struct. (THEOCHEM) 1984, 109, 251-269.
10. Gutman, I.; El-Basil, S. Topological Properties of Benzenoid Systems. XXXVII. Characterization of Certain Chemical Graphs. Z. Naturforsch. 1985, 40a, 923-926.
11. Gutman, I.; Polansky, O. E. Mathematical Concepts in Organic Chemistry; Springer-Verlag: Berlin, 1986.
12. Polansky, O. E.; Mark, G.; Zander, M. Der Topologische Effekt an Molekülorbitalen (TEMO); Max-Planck-Institut für Strahlenchemie: Mü̈lheim. 1987: pp 379-397.
13. Gutman, I.; Cyvin, S. J. Introduction to the Theory of Benzenoid Hydrocarbons: Springer-Verlag: Berlin, 1989; pp 108-114.
14. Diudea, M. V.; Horvath, D.; Kacso, I. E.; Minailiuc, O. M.; Parv, B. Molecular Topology. VIII: Centricities in Molecular Graphs. The MOLCEN Algorithm. J. Math. Chem. 1992, 11, 259-270.
15. Narumi, H.; Kita, H. Equivalent Bond Index. Commun. Math. Chem. (MATCH) 1994, 30, 225-242.
16. Diudea, M. V.; Horvath, D.; Bonchev, D. Molecular Topology. 14. Molord Algorithm and Real Number Subgraph Invariants. Croat. Chem. Acta 1995, 68, 131-148.
17. Estrada, E. Edge Adjacency Relationships and a Novel Topological Index Related to Molecular Volume. J. Chem. Inf. Comput. Sci. 1995, 35, 31-33.
18. Gutman, I.; Estrada, E. Topological Indices Based on the Line Graph of the Molecular Graph. J. Chem. Inf. Comput. Sci. 1996, 36, 541- 543.
19. Estrada E. Spectral Moments of the Edge Adjacency Matrix in Molecular Graphs. 1. Definition and Applications to the Prediction of Physical Properties of Alkanes. J. Chem. Inf. Comput. Sci. 1996, 36, 844-849.
20. Estrada, E.; Gutman, I. A Topological Index Based on Distances of Edges of Molecular Graphs. J. Chem. Inf. Comput. Sci. 1996, 36, 850- 853.
21. Estrada, E.; Ramírez, A. Edge Adjacency Relationships and Molecular Topographic Descriptors. Definition and QSAR Applications. J. Chem. Inf. Comput. Sci. 1996, 36, 837-843.
22. Estrada, E.; Guevara, N.; Gutman, I. Extension of Edge Connectivity Index. Relationships to Line Graph Indices and QSPR Applications. J. Chem. Inf. Comput. Sci. 1998, 38, 428-431.
23. Estrada, E.; Rodriguez, L. Edge-Connectivity Indices in QSPR/QSAR Studies. 1. Comparison to Other Topological Indices in QSPR Studies. J. Chem. Inf. Comput. Sci. 1999, 39, 1037-1041.
24. Estrada, E. Edge-Connectivity Indices in QSPR/QSAR Studies. 2. Accounting for Long-Range Bond Contributions. J. Chem. Inf. Comput. Sci. 1999, 39, 1042-1048.
25. Bertz, S. H. Branching in Graphs and Molecules. Discr. Appl. Math. 1988, 19, 65-83.
26. Bertz, S. H. A Mathematical Model of Molecular Complexity. Stud. Phys. Theor. Chem. 1993, 28, 206-221.
27. Gutman, I.; Popović, L.: Mishra, B. K.; Kuanar, M.; Estrada, E.; Guevara, N. Application of Line Graphs in Physical Chemistry. Predicting the Surface Tensions of Alkanes. J. Serb. Chem. Soc: 1997, 62, 1025-1029.
28. Gutman, I.; Popović, L.; Estrada, E.; Bertz, S. H. The Line Graph Model. Predicting Physico-Chemical Properties of Alkanes. ACH Models Chem. 1998, 135, 147-155.
29. Estrada, E. Generalized Spectral Moments of the Iterated Line Graphs Sequence. A Novel Approach to QSPR Studies. J. Chem, Inf. Comput. Sci. 1999, 39, 90-95.
30. Gutman, I.; Tomović, Z. On the Application of Line Graphs in Quantitative Structure-Property Studies. J. Serb. Chem. Soc. 2000, 65, 577-580.
31. Gutman, I.; Tomović, Z. More on the Line Graph Model for Predicting Physico-Chemical Properties of Alkanes. ACH Models Chem. 2000, 137, 439-445.
32. As pointed out by one of the referees (Dr. Christoph Rücker), the goal of such QSPR studies is not only to describe or predict a particular property for a particular series of compounds as exactly as possible in terms of simple graph invariants but also to find such graph invariants which are useful for a population of compounds as broad as possible and to learn something about the physical interpretation of invariants. In Rucker's opinion, it is to be suspected that the descriptors used here, the numbers of edges of the iterated line graphs, will encounter problems when used for a combined sample of unsubstituted and substituted cycloalkanes or for a sample of straightchain and branched acyclic alkanes, due to the drastically divergent behavior of these numbers for these closely related groups of compounds. We intend to examine these possible difficulties at a later moment. Another limitation of our structure-descriptors is that they cannot discriminate between isomeric regular graphs.
33. Harary, F. Graph Theory: Addison-Wesley: Reading, MA, 1969.
34. Buckley, F. Mean Distance in Line Graphs. Congr. Numer. 1981, 32, 153-162.
35. For instance, the Bertz indices of the following pairs of bicycloalkanes coincide until (at least) seventh order: I, I′ -bicyclopropyl and bicyclo[2.2.0]hexane, dicyclopropylmethane and bicyclo[2.2.1 jheptane, I. I′bicyclobutyl and bicyclo[3.3.0]octane, dicyclobutylmethane and bicyclo[3.3.l]nonane, etc.
36. 3
37. Czerminski, J.; Iwasiewicz, A.; Paszek, Z.; Sikorski, A. Statistical Methods in Applied Chemistry; Elsevier: Amsterdam, 1990.