The Szeged Index and an Analogy with the Wiener Index

Journal of Chemical Information and Computer Sciences

Volumn 35, Issue 3, 1995, Pages 547-550

  Khadikar, Padmakar V ^a   Deshpande, Narayan V ^a   Kale, Prabhakar P ^a   Dobrynin, Andrey ^b   Gutman, Ivan ^c   Domotor, Gyula ^c  

^a DEVI AHILYA UNIVERSITY   (India)

^b SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

^c UNIVERSITY OF SZEGED   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33751156690     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci00025a024     Document Type: Article

References (20)

1. Wiener, H. Structural Determination of Paraffin Boiling Points. J. Am. Chem. Soc. 1947, 69, 17-20.
2. There exist a large number of reviews and books dealing with the Wiener number and its chemical applications; we mention only the most recent ones3-7 in which references to earlier works can be found.
3. Mihalic, Z.; Veljan, D.; Amic, D.; Nikolic, S.; Plavsic, D.; Trinajstic, N. The Distance Matrix in Chemistry. J. Math. Chem. 1992, 11, 223-258.
4. 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.
5. Rouvray, D. H. In Applications of Mathematical Concepts to Chemistry; Trinajstic, N., Ed.; Horwood: Chichester, 1985.
6. Gutman, I.; Polansky, O. E. Mathematical Concepts in Organic Chemistry; Springer-Verlag: Berlin, 1986.
7. Trinajstic, N. Chemical Graph Theory, 2nd revised ed.; CRC Press: Boca Raton, FL, 1992.
8. Buckley, F.; Harary, F. Distance in Graphs; Addison-Wesley: Reading, MA, 1990.
9. Gutman, I. A new Method for the Calculation of the Wiener Number of Acyclic Molecules. J. Mol. Struct. (Theochem) 1993, 285, 137-142.
10. In Hungarian “sz” is pronounced as “s” in English. For instance, the Hungarian spelling of “September”, “software”, “sex”, and “story” is “szeptember”, “szoftver”, “szex”, and “sztori”, whereas the pronunciation (as well as the meaning) are essentially the same as in English.
11. Gutman, I. A. Formula for the Wiener Number of Trees and Its Extension to Graphs Containing Cycles. Graph Theorx Notes New York 1994. 27,9-15.
12. Dobrynin, A.; Gutman, I. Solving a Problem Connected with Distances in Graphs. Graph Theory Notes New York 1995, 28, in press.
13. Lukovits, I. Wiener Indices and Partition Coefficients of Unsaturated Hydrocarbons. Quant. Struct. Act. Relat. 1990, 9, 227-231.
14. Lukovits, I. Correlation between Components of the Wiener Index and Partition Coefficients of Hydrocarbons. Int. J. Quantum Chem. Quantum. Biol. Symp. 1992, 19, 217-223.
15. Randić, M. Novel Molecular Descriptor for Structure-Property Studies. Chem. Phys. Lett. 1993, 211, 478-483.
16. Mohar, B.; Babic, D.; Trinajstic, N. A. Novel Definition of the Wiener Index of Trees. J. Chem. Inf. Comput. Sci. 1993, 33, 153-154.
17. Randić. M.; Guo, X. F.; Oxley, T.; Krishnapriyan, H. Wiener Matrix–Source of Novel Graph Invariants. J. Chem. Inf. Comput. Sci. 1993, 33, 709-716.
18. 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.
19. Gutman, I. Wiener Numbers of Benzenoid Hydrocarbons: Two Theorems. Chem. Phys. Lett. 1987, 136, 134-136.
20. Recall that a catacondensed benzenoid hydrocarbon is a benzenoid hydrocarbon in which no carbon atoms belong to three six-membered rings. All catacondensed benzenoid hydrocarbons possessing an equal number (= h) of six-membered rings are isomers; they all have the same formula: For more details on this matter, see: Gutman, I.; Cyvin, S. J. Introduction to the Theory of Benzenoid Hydrocarbons’, Springer-Verlag: Berlin. 1989.