Character of graphs with extremal Balaban index

Match

Volumn 63, Issue 3, 2010, Pages 799-812

  Dong, Hawei ^a,b   Guo, Xiaofeng ^a  

^a XIAMEN UNIVERSITY   (China)

^b MINJIANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953263905     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (53)

1. A. T. Balaban, O. Ivanciuc, Historical development of topological indices, in: J. Devillers, A. T. Balaban (Eds.), Topological Indices and Related Descriotors in QSAR and QSPR, Gordon and Breach, 1999, pp. 21-57.
2. H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17-20.
3. M. Randić, On characterization of molecular branching, J. Am. Chem. Soc. 97 (1975) 6609-6615.
4. A. T. Balaban, Highly discriminating distance-based topological index, Chem. Phys. Lett. 89 (1982) 399-404.
5. A. T. Balaban, Topological indices based on topological distances in molecular graphs, Pure Appl. Chem. 55 (1983) 199-206.
6. X. Guo, M. Randić, Trees with the same topological index JJ, SAR and QSAR Environ. Res. 10 (1999) 381-394.
7. A. T. Balaban, A comparison between various topological indices, particularly between the index J and Wiener's index W, in: D. H. Rouvray, R. B. King (Eds.), Topology in Chemistry - Discrete Mathematics of Molecules, Horwood, Chichester, 2002, pp. 89-112.
8. A. T. Balaban, N. Ionescu-Pallas, T. S. Balaban, Asymptotic values of topological indices J and J' (average distance sum connectivities) for infinite cyclic and acyclic graphs, MATCH Commun. Math. Comput. Chem. 17 (1985) 121-146.
9. N. Jia, K. W. McLaughlin, Fibonacci trees: A study of the asymptotic behavior of Balaban's index, MATCH Commun. Math. Comput. Chem. 51 (2004) 79-95.
10. T. S. Balaban, A. T. Balaban, D. Bonchev, A topological approach to predicting properties of infiite polymers. Part VI. Rational formulas for the normalized Wiener index and a comparison with index J, J. Mol. Struct. (Theochem) 535 (2001) 81-92.
11. J. Devillers, A. T. Balaban (Eds.), Topological Indices and Related Descriptors in QSAR and QSPR, Gordon & Breach, Amsterdam, 1999.
12. M. P. Hanson, D. H. Rouvray, Novel applications of topological indices. 2. Prediction of the threshold soot index for hydrocarbon fuels, J. Phys. Chem. 91 (1987) 2981-2985.
13. M. Vedrina, S. Nikolić, M. Medić-Šarić, N. Trinajstić, TAM: a program for the calculation of topological indices in QSPR and QSAR studies, Computers Chem. 6 (1997) 355-361.
14. J. F. Caputo, K. J. Cook, A graph-theoretical approach to the prediction of physical properties of alkanes based on the distance matrix, Pharm. Res. 6 (1989) 809-812.
15. S. Gupta, M. Singh, A. K. Madan, Connective eccentricity index: a novel topological descriptor for predicting biological activity, J. Mol. Graphics Model. 18 (2000) 18-25.
16. M. Jalali-Heravi, M. H. Fatemi, Prediction of thermal conductivity detection response factors using an artificial neural network, J. Chromatogr. A 897 (2000) 227-235.
17. M. Jalali-Heravi, M. Asadollahi-Baboli, QSAR analysis of platelet-derived growth inhibitors using GA-ANN and shuffling crossvalidation, QSAR Comb. Sci. 27 (2008) 750-757.
18. f against descriptors of codessa, J. Chem. Inf. Model. 41 (2001) 631-638.
19. E. Estrada, Generalization of topological indices, Chem. Phys. Lett. 336 (2001) 248-252.
20. E. Estrada, Generalized graph matrix, graph geometry, quantum chemistry, and optimal description of physicochemical properties, J. Phys. Chem. A 107 (2003) 7482-7489.
21. E. Estrada, A. R. Matamala, GTI-space: the space of generalized topological indices, J. Math. Chem. 43 (2008) 508-517.
22. J. Zheng, Y. Polyakova, K. H. Row, Prediction of retention of nucleic compounds based on a QSPR model, Chromatographia 64 (2006) 1-9.
23. A. Krawczuk, A. Voelkel, J. Lulek, R. Urbaniak, K. Szyrwiska, Use of topological indices of polychlorinated biphenyls in structure-retention relationships, J. Chromatogr. A 1018 (2003) 63-71.
24. A. Ratkiewicz, T. N. Truong, Application of chemical graph theory for automated mechanism generation, J. Chem. Inf. Comput. Sci. 43 (2003) 36-44.
25. S. N. Rao, T. P. Stockfisch, Partially unified multiple property recursive partitioning (PUMP-RP) analyses of cyclooxygenase (COX) inhibitors, J. Chem. Inf. Comput. Sci. 43 (2003) 1614-1622.
26. J. M. Santiuste, Relationships between retention data of benzene and chlorobenzenes with their physico-chemical properties and topological indices, J. M. Takacs, Chromatographia 58 (2003) 87-96.
27. K. Roy, G. Ghosh, QSTR with extended topochemical atom indices. 4. Modeling of the acute toxicity of phenylsulfonyl carboxylates to vibrio fischeri using principal component factor analysis and principal component regression analysis, QSAR Comb. Sci. 23 (2004) 526-535.
28. C. Rücker, G. Rücker, M. Meringer, Exploring the limits of graph invariant- and spectrum-based discrimination of (sub) structures, J. Chem. Inf. Comput. Sci. 42 (2002) 640-650.
29. A. Jezierska, Counter-propagation artificial neural network as a tool for the independent variable selection: structure-mutagenicity study on aromatic amines, Mol. Divers. 8 (2004) 371-377.
30. H. Gonzalez-Diaz, G. Aguero, M. A. Cabrera, R. Molina, L. Santana, E. Uriarte, G. Delogu, N. Castanedo, Unified Markov thermodynamics based on stochastic forms to classify drugs considering molecular structure, partition system, and biological species: distribution of the antimicrobial G1 on rat tissues. Bioorg. Med. Chem. Lett. 15 (2005) 551-557.
31. M. R. McGillen, C. J. Perciva, T. Raventos-Duran, G. Sanchez-Reyn, D. E. Shallcross, Can topological indices be used to predict gas-phase rate coefficients of importance to tropospheric chemistry? Free radical abstraction reactions of alkanes, Atmospheric Env. 40 (2006) 2488-2500.
32. A. Panaye, J. P. Doucet, J. Devillers, N. Marchand-Geneste, J. M. Porcher, Decision trees versus support vector machine for classification of androgen receptor ligands, SAR QSAR Env. Res. 19 (2008) 129-151.
33. V. Rastija, M. Medric-Saric, QSAR Study of antioxidant activity of wine polyphenols, Eur. J. Med. Chem. 44 (2009) 400-408.
34. Y. Polyakova, M. Long, K. H. Row, Linear regression based QSPR models for the prediction of the retention mechanism of some nitrogen containing heterocycles, J. Liq. Chromatogr. Rel. Techn. 29 (2006) 533-552.
35. C. R. Munteanu, H. Gonzalez-Diaz, F. Borges, A. L. Magalhaes, Natural random protein classification models based on star network topological indices, J. Theo. Bio. 254 (2008) 775-783.
36. H. Dureja, A. K. Madan, Superaugmented eccentric connectivity indices: A new generation of highly discriminating topological descriptors for QSAR/QSPR modeling, Med. Chem. Res. 16 (2007) 331-341.
37. S. Prasanna, E. Manivannan, S. C. Chaturvedi, QSAR analyses of conformationally restricted 1, 5-diaryl pyrazoles as selective COX-2 inhibitors: application of connection table representation of ligands, Bioorg. Med. Chem. 15 (2005) 2097-2102.
38. A. Thakur, M. Thakur, P. V. Khadikar, C. T. Supuran, P. Sudele, QSAR study on benzenesulphonamide carbonic anhydrase inhibitors: topological approach using Balaban index, Bioorg. Med. Chem. 12 (2004) 789-793.
39. G. Grassy, B. Calas, A. Yasri, R. Lahana, J. Woo, S. Iyer, M. Kaczorek, R. Floc'h, R. Buelow, Computer-assisted rational design of immunosuppressive compounds, Nature Biotechnol. 16 (1988) 748-752.
40. C. Bermudex, E. E. Daza, E. Andrade, Characterization and comparison of Escherichia coli transfer RNA by graph theory based on secondary structure, J. Theor. Biol. 197 (1999) 193-205.
41. W. Shu, X. Bo, Z. Zheng, and S. Wang, A novel representation of RNA secondary structure based on element-contact graphs, BMC Bioinformatics 9 (2008) 188-196.
42. E. Estrada, Y. Gutierrez, The Balaban J index in the multidimensional space of generalized topological indices. Generalizations and QSPR improvements, MATCH Commun. Math. Comput. Chem. 44 (2001) 155-16.
43. A. A. Dobrynin, I. Gutman, S. Klavžar, P. žigert, Wiener index of hexagonal systems, Acta Appl. Math. 72 (2002) 247-294.
44. A. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math. 66 (2001) 211-249.
45. R. C. Entringer, D. E. Jackson, D. A. Snyder, Distance in graphs, Czech. Math. J. 26 (1976) 283-296.
46. J. Plesnik, On the sum of all distances in a graph or digraph, J. Graph Theory 8 (1984) 1-21.
47. I. Gutman, S. Zhang, Graph connectivity and Wiener index, Bull. Acad. Serbe Sci. Arts (Cl. Sci. Math. Natur.) 133 (2006) 1-5.
48. X. Li, Y. Shi, A survey on the Randić index, MATCH Commun. Math. Comput. Chem. 59 (2008) 127-156.
49. B. Zhou, N. Trinajstić, Bounds on the Balaban index, Croat. Chem. Acta. 81 (2008) 319-323.
50. C. Jordan, Sur les assemblages de lignes, J. Reine Angew. Math. 70 (1869) 185-190.
51. C. A. Barefoot, R. C. Entringer, L. A. Szely, External values for ratios of distance in trees, Discr. Appl. Math. 80 (1997) 37-56.
52. O. Ore, Diameters in graphs, J. Comb. Theory 5 (1968) 75-81.
53. R. D. Luce, Commectivity and generalized cliques in sociometric group structure, Psychometrika 15 (1950) 169-190.