Wiener Index Extension by Counting Even/Odd Graph Distances

Journal of Chemical Information and Computer Sciences

Volumn 41, Issue 3, 2001, Pages 536-549

  Ivanciuc, Ovidiu ^a   Ivanciuc, Teodora ^a   Klein, Douglas J ^a   Seitz, William A ^a   Balaban, Alexandru T ^a  

^a TEXAS A AND M UNIVERSITY AT GALVESTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE;

WIENER INDEX;

DATABASE SYSTEMS; ENTHALPY; GIBBS FREE ENERGY; GRAPH THEORY; REFRACTIVE INDEX; SPECIFIC HEAT; STRUCTURE (COMPOSITION); TOPOLOGY; VAPORIZATION;

ORGANIC COMPOUNDS;

EID: 0035353674     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci000086f     Document Type: Article

References (71)

1. Kier, L. B.; Hall, L. H. Molecular Connectivity in Chemistry and Drug Research; Academic Press: New York, 1976.
2. Kier, L. B.; Hall, L. H. Molecular Connectivity in Structure - Activity Analysis: Research Studies Press: Letchworth, U.K., 1986.
3. Trinajstić. N. Chemical Graph Theory, 2nd ed.; CRC Press: Boca Raton, FL, 1992.
4. Diudea, M. V.; Ivanciuc, O. Molecular Topology; Comprex: Cluj, Romania, 1995.
5. Balaban, A. T. From Chemical Graphs to 3D Molecular Modeling. In From Chemical Topology to Three-Dimensional Geometry: Balaban, A. T., Ed.; Plenum: New York, 1997; pp 1-24.
6. Diudea, M. V. Valencies of Property. Croat. Chem. Acta 1999, 72, 835-851.
7. Balaban, A. T. Local versus Global (i.e. Atomic versus Molecular) Numerical Modeling of Molecular Graphs. J. Chem. Inf. Comput. Sci. 1994, 34, 398-402.
8. Ivanciuc, O.; Balaban, A. T. Graph Theory in Chemistry. In The Encyclopedia of Computational Chemistry; Schleyer, P. v. R., Allinger, N. L., Clark, T., Gasteiger, J., Kollman, P. A., Schaefer, H. F., III, Schreiner, P. R., Eds.; John Wiley & Sons: Chichester, U.K., 1998; pp 1169-1190.
9. Balaban, A. T.; Ivanciuc, O. Historical Development of Topological Indices. In Topological Indices and Related Descriptors in QSAR and QSPR; Devillers, J., Balaban, A. T., Eds.; Gordon and Breach Science Publishers: Amsterdam, 1999; pp 21-57.
10. Ivanciuc, O.; Balaban, A. T. The Graph Description of Chemical Structures. In Topological Indices and Related Descriptors in QSAR and QSPR; Devillers, J., Balaban, A. T., Eds.; Gordon and Breach Science Publishers: Amsterdam, 1999; pp 59-167.
11. Ivanciuc, O.; Ivanciuc, T.; Balaban, A. T. Vertex- and Edge-Weighted Molecular Graphs and Derived Structural Descriptors. In Topological Indices and Related Descriptors in QSAR and QSPR: Devillers, J., Balaban, A. T., Eds.; Gordon and Breach Science Publishers: Amsterdam, 1999; pp 169-220.
12. Ivanciuc, O.; Ivanciuc, T. Matrices and Structural Descriptors Computed from Molecular Graph Distances. In Topological Indices and Related Descriptors in QSAR and QSPR: Devillers, J., Balaban, A. T., Eds.; Gordon and Breach Science Publishers: Amsterdam. 1999; pp 221-277.
13. Ivanciuc, O.; Ivanciuc, T.; Diudea, M. V. Molecular Graph Matrices and Derived Structural Descriptors. SAR QSAR Environ. Res. 1997, 7, 63-87.
14. Diudea, M. V.; Gutman, I. Wiener-Type Topological Indices. Croat. Chem. Acta 1998, 71, 21-51.
15. Estrada, E. Novel Strategies in the Search of Topological Indices. In Topological Indices and Related Descriptors in QSAR and QSPR; Devillers, J., Balaban, A. T., Eds.; Gordon and Breach Science Publishers: Amsterdam, 1999; pp 403-453.
16. Randić, M.; Hansen, P. J.; Jurs, P. C. Search for Useful Graph Theoretical Invariants of Molecular Structure. J. Chem. Inf. Comput. Sci. 1988, 28, 60-68.
17. Randić, M. Comparative Regression Analysis. Regressions Based on a Single Descriptor. Croat. Chem. Acta 1993, 66, 289-312.
18. Randić, M.; Mihalić, Z.; Nikolić, S.; Trinajstić, N. Graph-Theoretical Correlations - Artifacts or Facts? Croat. Chem. Acta 1993, 66, 411- 434.
19. Estrada, E.; Rodriguez, L. Edge-Connectivity Indices in QSPR/QSAR Studies. I. Comparison to Other Topological Indices in QSPR Studies. J. Chem. Inf. Comput. Sci. 1999, 39, 1037-1041.
20. Barysz, M.; Jashari, G.; Lall, R. S.; Srivastava, V. K.; Trinajstić, N. On the Distance Matrix of Molecules Containing Heteroatoms. In Chemical Applications of Topology and Graph Theory; King, R. B., Ed., Elsevier: Amsterdam, 1983; pp 222-227.
21. Balaban, A. T. Chemical Graphs, Part 48. Topological Index J for Heteroatom-Containing Molecules Taking Into Account Periodicities of Element Properties. MATCH (Commun. Math. Chem.) 1986, 21, 115-122.
22. Balaban, A. T.; Ivanciuc, O. FORTRAN 77 Computer Program for Calculating the Topological Index J for Molecules Containing Heteroatoms. In MATH/CHEM/COMP 1988. Proceedings of an International Course and Conference on the Interfaces between Mathematics. Chemistry and Computer Sciences, Dubrovnik, Yugoslavia, June 20- 25, 1988; Graovac, A., Ed.; Studies in Physical and Theoretical Chemistry; Elsevier: Amsterdam, 1989; Vol. 63, pp 193-212.
23. Balaban, A. T.; Ivanciuc, O. FORTRAN 77 Computer Program for Calculating the Topological Index J for Molecules Containing Heteroatoms. In MATH/CHEM/COMP 1988. Proceedings of an International Course and Conference on the Interfaces between Mathematics. Chemistry and Computer Sciences, Dubrovnik, Yugoslavia, June 20- 25, 1988; Graovac, A., Ed.; Studies in Physical and Theoretical Chemistry; Elsevier: Amsterdam, 1989; Vol. 63, pp 193-212.
24. Ivanciuc, O.; Ivanciuc, T.; Balaban A. T. Design of Topological Indices. Part 10, Parameters Based on Electronegativity and Covalent Radius for the Computation of Molecular Graph Descriptors for Heteroatom-Containing Molecules, J. Chem. Inf. Comput. Sci. 1998, 38, 395-401.
25. Grassy, G.; Calas, B.; Yasri, A.; Lahana, R.; Woo, J.; Iyer, S.; Kaczorek, M.; Floc'h, R.; Buelow, R. Computer-Assisted Rational Design of Immunosuppressive Compounds. Nature Biotechnol. 1998, 16, 748-752.
26. Wiener, H. Structural Determination of Paraffin Boiling Points. J. Am. Chem. Soc. 1947, 69, 17-20. Wiener, H. Correlation of Heats of Isomerization and Differences in Heats of Vaporization of 'Isomers among the Paraffin Hydrocarbons, J. Am. Chem. Soc. 1947, 69, 2636- 2638.
27. Wiener, H. Structural Determination of Paraffin Boiling Points. J. Am. Chem. Soc. 1947, 69, 17-20. Wiener, H. Correlation of Heats of Isomerization and Differences in Heats of Vaporization of 'Isomers among the Paraffin Hydrocarbons, J. Am. Chem. Soc. 1947, 69, 2636- 2638.
28. Hosoya, H. A Newly Proposed Quantity Characterising the Topological Nature of Structural Isomers of Saturated Hydrocarbons. Bull. Chem. Soc. Jpn. 1971, 44, 2332-2339.
29. Ivanciuc, O. Design on Topological Indices, 1. Definition of a Vertex Topological Index in the Case of 4-Trees. Rev. Roum. Chim. 1989, 34, 1361-1368.
30. Balaban, T. S.; Filip, P. A.; Ivanciuc, O. Computer Generation of Acyclic Graphs Based on Local Vertex Invariants and Topological Indices, Derived Canonical Labelling and Coding of Trees and Alkanes. J. Math. Chem. 1992, 11, 79-105.
31. 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.
32. Ivanciuc, O.; Balaban, T.-S.; Balaban, A. T. Design of Topological Indices. Part 4. Reciprocal Distance Matrix, Related Local Vertex Invariants and Topological Indices. J. Math. Chem. 1993, 12, 309- 318.
33. Diudea, M. V.; Ivanciuc, O.; Nikolić, S.; Trinajstić, N. Matrices of Reciprocal Distance, Polynomials and Derived Numbers. MATCH (Commun. Math. Comput. Chem.) 1997, 35, 41-64.
34. Klein, D. J.; Randić, M. Resistance Distance. J. Math. Chem. 1993, 12, 81-95.
35. Ivanciuc, O.; Balaban, A. T. Design of Topological Indices. Part 8. Path Matrices and Derived Molecular Graph Invariants. MATCH (Commun, Math. Chem.) 1994, 30, 141-152.
36. Ivanciuc, O. Design of Topological Indices. Pan 11. Distance-Valency Matrices and Derived Molecular Graph Descriptors. Rev. Roum. Chim. 1999, 44, 619-631.
37. Ivanciuc, O.; Ivanciuc, T.; Balaban, A. T. The Complementary Distance Matrix, a New Molecular Graph Metric. ACH - Models Chem. 2000, 137, 57-82.
38. Hosoya, H. On Some Counting Polynomials in Chemistry. Discrete Appl. Math. 1988, 19, 239-257.
39. Sagan, B. E.; Yeh, Y.-N.; Zhang, P. The Wiener Polynomial of a Graph. Int. J. Quantum Chem. 1996, 60, 959-969.
40. Estrada, E.; Ivanciuc, O.; Gutman, I.; Gutierrez, A.; Rodríguez, L. Extended Wiener Indices. A New Set of Descriptors for Quantitative Structure-Property Studies. New J. Chem. 1998, 22, 819-822
41. Lepović, M.; Gutman, I. A Collective Property of Trees and Chemical Trees. J. Chem. Inf. Comput. Sci. 1998, 38, 823-826.
42. Randić, M. Novel Molecular Descriptor for Structure - Property Studies. Chem. Phys. Lett. 1993, 211, 478-483.
43. Randić, M.; Quo, X.; Oxley, T.; Krishnapriyan, H. Wiener Matrix: Source of Novel Graph Invariants. J. Chem. Inf. Comput. Sci. 1993, 33, 709-716.
44. 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.
45. Ivanciuc, O.; Diudea, M. V.; Khadikar, P. V. New Topological Matrices and Their Polynomials. Ind. J. Chem. 1998, 37A, 574-585.
46. Ivanciuc, O.; Taruviras, S. L.; Cabrol-Bass, D. Quasi-Orthogonal Basis Sets of Molecular Graph Descriptors as a Chemical Diversity Measure. J. Chem. Inf. Comput. Sci. 2000, 40, 126-134.
47. Taraviras, S. L.; Ivanciuc, O.; Cabrol-Bass, D. Identification of Groupings of Graph Theoretical Molecular Descriptors Using a Hybrid Cluster Analysis Approach. J. Chem. Inf. Comput. Sci. 2000, 40, 1128-1146.
48. Zhu, H.-Y.; Klein, D. J.; Lukovits, I. Extensions of the Wiener Number. J. Chem. Inf. Comput. Sci. 1996, 36, 420-428.
49. Klein, D. J.; Gutman, I. Wiener-Number-Related Sequences. J. Chem. Inf. Comput. Sci. 1999, 39, 534-536.
50. Estrada, E.; Rodríguez, L.; Gutiérrez, A. Matrix Algebraic Manipulation of Molecular Graphs. I. Distance and Vertex-Adjacency Matrices. MATCH (Commun. Math. Comput. Chem.) 1997, 35, 145-156.
51. Estradu, E.; Rodríguez, L. Matrix Algebraic Manipulation of Molecular Graphs. 2. Harary- and MTI-Like Molecular Descriptors. MATCH (Commun. Math. Comput. Chem.) 1997, 35, 157-167.
52. Zhu, H.-Y.; Klein, D. J. Graph-Geometric Invariants for Molecular Structures. J. Chem. Inf. Comput. Sci. 1996, 36, 1067-1075.
53. Klein, D. J. Graph Geometry, Graph Metrics, & Wiener, MATCH (Commun. Math. Comput. Chem.) 1997, 35, 7-27.
54. Klein, D. J.; Zhu, H.-Y. Distances and Volumina for Graphs. J. Math. Chem., 1998, 23, 179-195.
55. Bytautas, L.; Klein, D. J. Chemical Combinatorics for Alkane-Isomer Enumeration and More. J. Chem. Inf. Comput. Sci. 1998, 38, 1063- 1078.
56. Bytautas, L.; Klein, D. J. Mean Wiener Numbers and Other Mean Extensions for Alkane Trees. J. Chem. Inf. Comput. Sci. 2000, 40, 471-481.
57. Balaban, A. T.; Balaban, T.-S. New Vertex Invariants and Topological Indices of Chemical Graphs Based on Information on Distances. J. Math, Chem. 1991, 8, 383-397.
58. Ivanciuc, O.; Balaban, T.-S.; Balaban, A. T. Chemical Graphs with Degenerate Topological Indices based on Information on Distances. J. Math. Chem. 1993, 14, 21-33.
59. Ivanciuc, O.; Laidboeur, T.; Cabrol-Bass, D. Degeneracy of Topologic Distance Descriptors for Cubic Molecular Graphs: Examples of Small Fullerenes, J. Chem. Inf. Comput. Sci. 1997, 37, 485-488.
60. Ivanciuc, O.; Balaban, A. T. Design of Topological Indices. Part 20. Molecular Structure Descriptors Computed with Information on Distances Operators. Rev. Roum. Chim. 1999, 44, 479-489.
61. Ivanciuc, O.; Balaban, A. T. Design of Topological Indices. Part 21. Molecular Graph Operators for the Computation of Geometric Structural Descriptors. Rev. Roum. Chim. 1999, 44, 539-547.
62. Ivanciuc, O.; Ivanciuc, T.; Cabrol-Bass, D.; Balaban, A. T. Evaluation in Quantitative Structure - Property Relationship Models of Structural Descriptors Derived from Information-Theory Operators. J. Chem. Inf. Comput. Sci. 2000, 40, 631-643.
63. Ivanciuc, O.; Ivanciuc, T.; Cabrol-Bass, D.; Balaban, A. T. Comparison of Weighting Schemes for Molecular Graph Descriptors: Application in Quantitative Structure - Retention Relationship Models for Alkyl phenols in Gas - Liquid Chromatography. J. Chem. Inf. Comput. Sci. 2000, 40, 732-743.
64. Gakh, A. A.; Gakh, E. G.; Sumpter, B. G.; Noid, D. W. Neural Network-Graph Theory Approach to the Prediction of the Physical Properties of Organic Compounds. J. Chem. Inf. Comput. Sci. 1994, 34, 832-839.
65. Ivanciuc, O. Artificial Neural Networks Applications. Part 9. MolNet Prediction of Alkane Boiling Points. Rev. Roum. Chim. 1998, 43, 885- 894.
66. Ivanciuc, O. The Neural Network MolNet Prediction of Alkane Enthalpies. Anal. Chim. Acta 1999, 384, 271-284.
67. Ivanciuc, O. Artificial Neural Networks Applications, Part 10. MolNet Prediction of Alkane Gibbs Energies, Rev. Roum. Chim. 1999, 44, 299-309.
68. Ivanciuc. O. Artificial Neural Networks Applications. Part 11. MolNet Prediction of Alkane Densities. Rev. Roum. Chim. 1999, 44, 619- 631.
69. Randić, M. On Characterization of Molecular Branching. J. Am. Chem. Soc. 1975, 97, 6609-6615.
70. Diudea, M. V.; Minailiuc, O.; Balaban, A. T. Molecular Topology. IV. Regressive Vertex Degrees (New Graph Invariants) and Derived Topological Indices. J. Comput. Chem. 1991, 12, 527-535.
71. Balaban, A. T.; Diudea, M. V. Real Number Vertex Invariants: Regressive Distance Sums and Related Topological Indices. J. Chem. Inf. Comput. Sci. 1993, 33, 421-428.