Formula for calculating the wiener index of catacondensed benzenoid graphs

Journal of Chemical Information and Computer Sciences

Volumn 38, Issue 5, 1998, Pages 811-814

  Dobrynin, Andrey A ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009884312     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci970450j     Document Type: Article

References (37)

1. Wiener, H. Structural determination of paraffin boiling points. J. Am. Chem. Soc. 1947, 68, 17-20.
2. Commun. Math. Chem. (MATCH) 1997, 35.
3. J. Serb. Chem. Soc. 1997, 62, 3.
4. Discrete Appl. Math. 1997, 80.
5. Bonchev, D. Information Theoretic Indices for Characterization of Chemical Structure; Research Studies Press: Chichester, U.K., 1983.
6. Trinajstić, N. Chemical Graph Theory; CRC Press: Boca Raton, FL, 1983; 2nd edition, 1992.
7. Gutman, I.; Polansky, O. E. Mathematical Concepts in Organic Chemistry; Springer-Verlag: Berlin, 1986.
8. Chemical Graph Theory-Introduction and Fundamentals; Bonchev, D., Rouvray, D. H., Eds.; Gordon & Breach: New York, 1991.
9. Rouvray, D. H. Should we have designs on topological indices? In Chemical Applications of Topology and Graph Theory; King, R. B., Ed.; Elsevier: Amsterdam, 1983; pp 159-177.
10. Canfield, E. R.; Robinson, R. W.; Rouvray, D. H. Determination of the Wiener molecular branching index for the general tree. J. Comput. Chem. 1985, 6, 598-609.
11. 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.
12. Nikolić, S.; Trinajstić, N.; Mihalić, Z. The Wiener index: Developments and applications. Croat. Chem. Acta 1995, 68, 105-129.
13. Plesnik, J. On the sum of all distances in a graph or digraph. J. Graph Theory 1984, 8, 1-21.
14. 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.
15. Mohar, B.; Pisanski, T. How to compute the Wiener index of a graph. J. Math. Chem. 1988, 2, 267-277.
16. Lukovits, I.; Gutman, I. Edge-decomposition of the Wiener number. Commun. Math. Chem. (MATCH) 1994, 31, 133-144.
17. John, P. E. Calculation of the Wiener index for a simple polytree. Commun. Math. Chem. (MATCH) 1994, 31, 123-132.
18. Juvan, M.; Mohar, B.; Graovac, A.; Klavžar, S.; Žerovnik, J. Fast computation of the Wiener index of fasciagraphs and rotagraphs. J. Chem. Inf. Comput. Sci. 1995, 35, 834-840.
19. Juvan, M.; Mohar, B. Bond contributions to the Wiener index. J. Chem. Inf. Comput. Sci. 1995, 35, 217-219.
20. Klavžar, S.; Gutman, I.; Mohar, B. Labeling of benzenoid systems which reflects the vertex-distance relations. J. Chem. Inf. Comput. Sci. 1995, 35, 590-593.
21. Senn, P. The computation of the distance matrix and the Wiener index for graphs of arbitrary complexity with weighted vertices and edges. Comput. Chem. 1988, 12, 219-227.
22. Mihalić, Z.; Veljan, D.; Amić, D.; Nikolić, S.; Plavšić, D.; Trinajstić, N. The distance matrix in chemistry. J. Math. Chem. 1992, 11, 223-258.
23. Gutman, I. Calculating the Wiener number: The Doyle-Graver method. J. Serb. Chem. Soc. 1993, 58 (10), 745-750.
24. Gutman, I. A new method for the calculation of the Wiener number of acyclic molecules. J. Mol. Struct. (THEOCHEM) 1993, 285, 137-142.
25. Dobrynin, A. A. A new formula for the calculation of the Wiener index of hexagonal chains. Commun. Math. Chem. (MATCH) 1997, 35, 75-90.
26. Chepoi, V.; Klavžar, S. Distances in benzenoid systems: Further developments; Preprint series; University of Ljubljana: Ljubljana, 1997; Vol. 35, p 540.
27. Chepoi, V.; Klavžar, S. The Wiener index and the Szeged index of benzenoid systems in linear time. J. Chem. Inf. Comput. Sci. 1997, 37, 752-755.
28. Chepoi, V. On distances in benzenoid graphs. J. Chem. Inf. Comput. Sci. 1996, 36, 1169-1172.
29. Gutman, I.; Klavžar, S. A method for calculating Wiener numbers of benzenoid hydrocarbons. Acta Chim. Hung. 1996, 133, 389-399.
30. Klavžar, S.; Gutman, I. Wiener number of vertex-weighted graphs and a chemical application. Discrete Appl. Math. 1997, 80, 73-81.
31. Dobrynin, A. A. A simple formula for the calculation of the Wiener index of hexagonal chains. Submitted for publication.
32. Gutman, I.; Cyvin, S. J. Introduction to the Theory of Benzenoid Hydrocarbons; Springer-Verlag: Berlin, 1989.
33. Balaban, A. T.; Harary, F. Chemical graphs. V. Enumeration and proposed nomenclature of benzenoid catacondensed polycyclic aromatic hydrocarbons. Tetrahedron 1968, 24, 2505-2516.
34. Gutman, I.; Polansky, O. E. Wiener numbers of polyacenes and related benzenoid molecules. Commun. Math. Chem. (MATCH) 1986, 20, 115-123.
35. Gutman, I. Wiener numbers of benzenoid hydrocarbons: Two theorems. Chem. Phys. Lett. 1987, 136, 134-136.
36. Gutman, I. On distances in some bipartite graphs. Publ. Inst. Math. (Beograd) 1988, 43, 3-8.
37. Dobrynin, A. A. Graph distance of catacondensed hexagonal polycyclic systems under its transformations. Vychisl. Sist. (in Russian) 1988, 127, 3-39.