The most private features of the topological index

Abstract

The detailed birth and growth history of the topological index (TI) is described by the author who himself proposed the the term TI and introduced its QSAR property of hydrocarbon molecules.

Keywords

• Hosoya-index,Z-index,godfather,QSAR

References

1. H. Hosoya, Internet Electronic J. Mol. Design, 1 (2002) 428-442.
2. H. Wiener, J. Am. Chem. Soc., 69 (1947) 17-20.
3. J. R. Platt, J. Phys. Chem., 56 (1952) 328-336.
4. H. Hosoya, Bull. Chem. Soc. Jpn., 44 (1971) 2332-2339.
5. I. Gutman, M. Milun, N. Trinajstic, Math. Chem. (Mülheim/Ruhr), 1 (1975) 171-175.
6. J.-I. Aihara, J. Amer. Chem. Soc., 98 (1976) 2750-2758.
7. E. J. Farrell, J. Comb. Theory, 26B (1979) 111-xxx; 27B (1979) 75-86.
8. A. T. Balaban, J. Comput. Chem., Japan, 16 (2017) 33-37.

9. J. Devillers, A. T. Balaban (Eds.), Topological indices and related descriptors in QSAR and QSPR,” Gordon Breach, Amsterdam (1999).
10. O. Ivanciuc, A. T. Balaban, in Chpter 3 of Ref. [9].
11. Special issue of Interelectronic J. of Molecular Design, 1 (2002), BioChem Press.
12. L. B. Kier, L. H. Hall, Molecular connectivity in chemistry and drug research, Academic Press, New York (1976).
13. M. Karelson, Molecular descriptors in QSAR/QSPR, Wiley, New York (2000).
14. H. Hosoya, Discrete Appl. Math., 19 (1988) 239-257.
15. I. Gutman, E. Estrada, O. Ivanciuc, Graph Theory Notes N. Y., 36 (1999) 7-13.
16. H. Hosoya, M. Murakami, M. Gotoh, Natl. Sci. Rept. Ochanomizu Univ., 24 (1973) 27-34.
17. R. L. Graham, L. Lovasz, Adv. Math., 29 (1978) 60-88.
18. R. L. Graham, A. J. Hoffman, H. Hosoya, J. Graph Theory, 1 (1977) 85-88.
19. H. Hosoya, F. Harary, J. Math. Chem., 12 (1993) 211-218.
20. H. Hosoya, K. Hosoi, I. Gutman, Theor. Chim. Acta, 38 (1975) 37-47.
21. H. Hosoya, Fibonacci Quarterly, 11 (1973) 255-266.
22. T. Koshy, Fibonacci and Lucas numbers with applications, Wiley, New York (2001).
23. Wikipedia, Chebyshev polynomials.
24. Wikipedia, Hermite polynomial.
25. WolframMathWorld, Hermite polynomial.
26. H. Hosoya, Natl. Sci. Rept. Ochanomizu Univ., 32 (1981) 127-138.
27. H. Hosoya, J. Chem. Documentation, 12 (1972) 181-183.
28. A. Mowshowitz, M. Dehmer, Entropy (Basel), 17 (2015) 1054-1062.
29. T. Aurues, Kokyuroku of Res. Inst. Math. Sci. Kyoto Univ., 1852 (2013) 165-176.
30. H. Hosoya, Topological index––New mathematics bridging from Fibonacci numbers to Pythagorean triangles––, (in Nihongo), Nihon-Hyoronsha, Tokyo (2012).