On Harary index

Journal of Mathematical Chemistry

Volumn 44, Issue 2, 2008, Pages 611-618

  Zhou, Bo ^a   Cai, Xiaochun ^a   Trinajstić, Nenad ^b  

^a SOUTH CHINA NORMAL UNIVERSITY   (China)

^b RUDER BO KOVI INSTITUTE   (Croatia)

Author keywords

Harary index; Harary matrix; Quandrangle free graphs; Triangle free graphs; Wiener index

Indexed keywords

EID: 48349115049     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-007-9339-2     Document Type: Article

References (29)

1. Plavšić D., Nikolić S., Trinajstić N., Mihalić Z (1993). On the Harary index for the characterization of chemical graphs. J. Math. Chem. 12: 235-250
2. Ivanciuc O., Balaban T.S., Balaban A.T. (1993) Reciprocal distance matrix, related local vertex invariants and topological indices. J. Math. Chem. 12: 309-318
3. O. Ivanciuc and A.T. Balaban, The graph description of chemical structures. in Topological Indices and Related Descriptors in QSAR and QSPR, ed. by J. Devillers, A.T. Balaban (Gordon & Breach, Amsterdam, 1999), pp. 59-167
4. M.V. Diudea, M.S. Florescu, P.V. Khadikar, Molecular Topology and Its Applications (EfiCon Press, Bucharest, 2006), p. 57
5. D. Janežič, A. Miličević, S. Nikolić, N. Trinajstić, Graph Theoretical Matrices in Chemistry (Mathematical Chemistry Monographs No. 3, University of Kragujevac, Kragujevac, 2007)
6. Hosoya H. (1971) Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull. Chem. Soc. Japan 44: 2332-2339
7. Wiener H. (1947) Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69: 17-20
8. Ivanciuc O., Ivanciuc T., Balaban A.T. (1998) Design of topological indices Part 10 Parameters based on electronegativity and vovalent radius for the computation of molecular graph descriptors for heteroatom-containing molecules. J. Chem. Inf. Comput. Sci. 38, 395-401
9. Diudea M.V. (1997) Indices of reciprocal properties or Harary indices. J. Chem. Inf. Comput. Sci. 37: 292-299
10. Lučić B., Miličević A., Nikolić S., Trinajstić N. (2002) Harary index-twelve years later. Croat. Chem. Acta 75: 847-868
11. J. Devillers, A.T. Balaban (eds.), Topological Indices and Related Descriptors in QSAR and QSPR (Gordon & Breach, Amsterdam, 1999)
12. R. Todeschini, V. Consonni, Handbook of Molecular Descriptors (Wiley-VCH, Weinheim, 2000)
13. Mihalić Z., Trinajstić N. (1992) A graph-theoretical approach to structure-property relationships. J. Chem. Educ. 69: 701-712
14. Ivanciuc O. (2000) QSAR comparative study of Wiener descriptors for weighted molecular graphs. J. Chem. Inf. Comput. Sci. 40: 1412-1422
15. Lučić B., Lukovits I., Nikolić S., Trinajstić N. (2001) Distance-related indexes in the quantitative structure-property relationship modeling. J. Chem. Inf. Comput. Sci. 41, 527-535
16. Trinajstić N., Nikolić S., Basak S.C., Lukovits I. (2001) Distance indices and their hyper-counterparts: Intercorrelation and use in the structure-property modeling. SAR QSAR Environ. Res. 12: 31-54
17. Nordhaus E.A., Gaddum J.W. (1956) On complementary graphs. Amer. Math. Monthly 63, 175-177
18. Trinajstić N. (1992) Chemical Graph Theory, 2nd revised edn. CRC press, Boca Raton
19. Gutman I., Trinajstić N. (1972) Graph theory and molecular orbitals. III. Total π-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17, 535-538
20. Nikolić S., Kovačević G., Miličević A., Trinajstić N. (2003) The Zagreb indices 30 years after. Croat. Chem. Acta 76, 113-124
21. Gutman I., Das K.C. (2004) The first Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem. 50, 83-92
22. Zhou B., Gutman I. (2004) Relationships between Wiener, hyper-Wiener and Zagreb indices. Chem. Phys. Lett. 394, 93-95
23. Zhou B., Stevanović D. (2006) A note on Zagreb indices. MATCH Commun. Math. Comput. Chem. 56, 571-578
24. Gutman I. (1997) A property of the Wiener number and its modifications. Indian J. Chem. 36A: 128-132
25. R.J. Wilson, Introduction to Graph Theory (Oliver & Boyd, Edinburgh, 1972), p. 46
26. D.M. Cvetković, M. Doob, H. Sachs, Spectra of Graphs-Theory and Application (Johann Ambrosius Barth, Heidelberg, 1995)
27. B. Zhou, N. Trinajstić, On the maximum eigenvalues of the reciprocal distance matrix and the reverse Wiener matrix. Int. J. Quantum Chem. (in press)
28. Zhang L., Wu B. (2005) The Nordhaus-Gaddum-type inequalities for some chemical indices. MATCH Commun. Math. Comput. Chem. 54, 183-194
29. F. Harary, Graph Theory, 2nd edn. (Addison-Wesley, Reading, PA, 1971)