Three methods for calculation of the hyper-Wiener index of molecular graphs

Journal of Chemical Information and Computer Sciences

Volumn 42, Issue 3, 2002, Pages 571-576

  Cash, Gordon ^c   Klavžar, Sandi ^a   Petkovšek, Marko ^b  

^a UNIVERSITY OF MARIBOR   (Slovenia)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

^c U S ENVIRONMENTAL PROTECTION AGENCY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL INDICES;

GRAPH THEORY; INTERPOLATION; MATHEMATICAL MODELS; MOLECULAR GRAPHICS; POLYNOMIALS;

ORGANIC COMPOUNDS;

EID: 0036589084     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci0100999     Document Type: Article

References (30)

1. Randić, M. Novel molecular descriptor for structure-property studies. Chem. Phys. Lett. 1993, 211, 478-483.
2. Randić M.; Guo, X.; Oxley, T.; Krishnapriyan, H. Wiener matrix: Source of novel graph invariants. J. Chem. Inf. Comput. Sci. 1993, 33, 709-716.
3. Lukovits, I.; Linert, W. A novel definition of the hyper-Wiener index for cycles. J. Chem. Inf. Comput. Sci. 1994, 34, 899-902.
4. 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.
5. Linert, W.; Renz, F.; Kleestorfer, K.; Lukovits, I. An algorithm for the computation of the hyper-Wiener index for the characterization and discrimination of branched acyclic molecules. Comput. Chem. 1995, 19, 395-401.
6. Diudea, M.V. Wiener and hyper-Wiener numbers in a single matrix. J. Chem. Inf. Comput. Sci. 1996, 36, 833-836.
7. 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.
8. Gutman, I. A property of the Wiener number and its modifications. Indian J. Chem. 1997, 36A, 128-132.
9. Diudea, M.V.; Gutman, I. Wiener-type topological indices. Croat. Chem. Acta 1998, 71, 21-51.
10. Dobrynin, A.A.; Gutman, I.; Piottukh-Peletskii, V.N. Hyper-Wiener index for acyclic structures. J. Struct. Chem. 1999, 40, 293-298.
11. Plavšić, D.; Lers, N.; Sertić-Bionda, K. On the relation between W'/W index, hyper-Wiener index, and Wiener number. J. Chem. Inf. Comput. Sci. 2000, 40, 516-519.
12. Gutman, I.; Cyvin, S.J. Introduction to the Theory of Benzenoid Hydrocarbons; Springer-Verlag: Berlin, 1989.
13. Berris, B.C.; Hovakeemian, G.H.; Lai, Y.-H.; Mestdagh, H.; Vollhardt, K.P.C. A new approach to the construction of biphenylenes by the cobalt-catalyzed cocyclization of o-diethynylbenzenes with alkynes. Application to an iterative approach to [3]phenylene, the first member of a novel class of benzocyclobutadienoid hydrocarbons. J. Am. Chem. Soc. 1985, 107, 5670-5687.
14. 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.
15. Gutman, I.; Klavžar, S. A method for calculationg Wiener numbers of benzenoid hydrocarbons and phenylenes. ACH Models Chem. 1996, 133, 389-399.
16. Klavžar, S.; Gutman, I.; Rajapakse, A. Wiener numbers of pericondensed benzenoid hydrocarbons, Croat. Chem. Acta 1997, 70, 979-999.
17. 1-embeddable planar graphs. Discrete Appl. Math. 1997, 80, 3-19.
18. Imrich, W.; Klavžar, S. Product Graphs: Structure and Recognition; John Wiley & Sons: New York, 2000.
19. 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.
20. Chepoi, V.; Klavžar, S. Distances in benzenoid systems: Further developments. Discrete Math. 1998, 192, 27-39.
21. Winkler, P. Isometric embeddings in products of complete graphs. Discrete Appl. Math. 1984, 7, 221-225.
22. Klavžar, S. Applications of isometric embeddings to chemical graphs. DIMACS Ser. Discr. Math. Theor. Comput. Sci. 2000, 51, 249-258.
23. Klavžar, S.; Žigert, P.; Gutman, I. An algorithm for the calculation of the hyper-Wiener index of benzenoid hydrocarbons. Comput. Chem. 2000, 24, 229-233.
24. Žigert, P.; Klavžar, S.; Gutman, I. Calculating the hyper-Wiener index of benzenoid hydrocarbons. ACH Models Chem. 2000, 137, 83-94.
25. Gutman, I. The topological indices of linear phenylenes. J. Serb. Chem. Soc. 1995, 60(2), 99-104.
26. Cash, G.G. Polynomial expressions for the hyper-Wiener index of extended hydrocarbon networks. Comput. Chem. 2001, 25, 577-582.
27. Hosoya, H. On some counting polynomials in chemistry. Discrete Appl. Math. 1988, 19, 239-257.
28. Cash, G.G. Relationship between the Hosoya polynomial and the hyper-Wiener index. Appl. Math. Lett. 2002, 15, in press.
29. Stevanović, D. Hosoya polynomial of composite graphs. Discrete Math. 2001, 235, 237-244.
30. Gutman, I.; Klavžar, S.; Petkovšek, M.; Žigert, P. On Hosoya polynomials of benzenoid graphs. Commun. Math. Chem. (MATCH) 2001, 43, 49-66.