New polynomial-based molecular descriptors with low degeneracy

PLoS ONE

Volumn 5, Issue 7, 2010, Pages

  Dehmer, Matthias ^a   Mueller, Laurin A J ^a   Graber, Armin ^a  

^a UNIVERSITY FOR HEALTH SCIENCES   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COMPUTER PROGRAM; CONTROLLED STUDY; DATA BASE; INFORMATION POLYNOMIAL; INTERMETHOD COMPARISON; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MOLECULAR DYNAMICS; PROBABILITY; RELIABILITY; SENSITIVITY ANALYSIS; STATISTICAL ANALYSIS; STATISTICAL DISTRIBUTION; STRUCTURE ANALYSIS; ALGORITHM; CHEMICAL MODEL; FACTUAL DATABASE; THEORETICAL MODEL;

ALGORITHMS; DATABASES, FACTUAL; MODELS, CHEMICAL; MODELS, THEORETICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED;

EID: 77955618668     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0011393     Document Type: Article

References (52)

1. Bang-Jensen J, Gutin G (2002) Digraphs. Theory, Algorithms and Applications. London, Berlin, Heidelberg: Springer.
2. Bonchev D, Rouvray DH (1991) Chemical Graph Theory. Introduction and Fundamentals. New York, NY, USA: Abacus Press.
3. Dong FM, Koh K.M, Teo KL (2005) Chromatic Polynomials and Chromaticity of Graphs World Scientific Publishing Company.
4. Gutman I (1991) Polynomials in graph theory. In: Bonchev D, Rouvray DH, eds. Chemical Graph Theory Introduction and Fundamentals, Abacus Press. Pp 133-176.
5. Pachter L, Sturmfels B (2005) Algebraic Statistics for Computational Biology Cambridge University Press.
6. Ellis-Monaghan JA, Merino C (2010, to appear) Graph polynomials and their applications i: The tutte polynomial. In: Dehmer M, ed. Structural Analysis of Complex Networks. Boston/Basel: Birkhäuser.
7. Bonchev D, Trinajstić N (1977) Information theory, distance matrix and molecular branching. J Chem Phys 67: 4517-4533.
8. Diudea MV, Gutman I, Jäntschi L (2001) Molecular Topology. Nova Publishing. New York, NY, USA.
9. Ivanciuc O, Ivanciuc T, Diudea MV (1999) Polynomials and spectra of molecular graphs. Roumanian Chemical Quanterly Reviews 7: 41-67.
10. Cvetkovic DM, Doob M, Sachs H (1997) Spectra of Graphs. Theory and Application Academic Press.
11. Hosoya H (1988) On some counting polynomials. Discrete Applied Mathematics 19: 239-257.
12. Randić M, Vracko M, Novic M (2001) Eigenvalues as molecular descriptors. In: Diudea MV, ed. QSPR/QSAR Studies by Molecular Descriptors, Nova Publishing. pp 93-120.
13. Lovász L, Pelikán J (1973) On the eigenvalues of trees. Periodica Mathematica Hungarica 3: 175-182.
14. Todeschini R, Consonni V, Mannhold R (2002) Handbook of Molecular Descriptors. Weinheim, Germany: Wiley-VCH.
15. Robles-Kelly A, Hancock R (2005) Graph edit distance from spectral seriation. IEEE Transactions on Pattern Analysis and Machine Intelligence 27: 365-378.
16. Mason O, Verwoerd M (2007) Graph theory and networks in biology. IET Systems Biology 1: 89-119.
17. Wasserman S, Faust K (1994) Social Network Analysis: Methods and Applications. Structural Analysis in the Social Sciences Cambridge University Press.
18. Estrada E (2002) Characterization of the folding degree of proteins. Bioinformatics 18: 697-704.
19. Chen SJ, Dill KA (1996) Symmetries in proteins: A knot theory approach. J Chem Phys 104: 5964-5973.
20. Emmert-Streib F (2006) Algorithmic computation of knot polynomials of secondary structure elements of proteins. Journal of Computational Biology 13:1503-1512.
21. Cover TM, Thomas JA (2006) Elements of Information Theory. Wiley Series in Telecommunications and Signal Processing Wiley & Sons.
22. Mignotte M, Stefanescu D (1999) Polynomials: An Algorithmic Approach Discrete Mathematics and Theoretical Computer Science Springer.
23. Fukui M, Kamae T (1984) Information polynomials of graphs. In: Akiyama J, ed. Number Theory and Combinatorics, World Scientific Publishing. Pp 97-104.
24. Kamae R (1983) Information of relative pairwise comparisons. Journal of Mathematical Analysis and Applications 92: 355-373.
25. Bonchev D (1983) Information Theoretic Indices for Characterization of Chemical Structures. Chichester: Research Studies Press.
26. Dehmer M, Emmert-Streib F (2008) Structural information content of networks: Graph entropy based on local vertex functionals. Comput Biol Chem 32: 131-138.
27. Dehmer M, Varmuza K, Borgert S, Emmert-Streib F (2009) On entropy-based molecular descriptors: Statistical analysis of real and synthetic chemical structures. J Chem Inf Model 49: 1655-1663.
28. Mowshowitz A (1968) Entropy and the complexity of the graphs I: An index of the relative complexity of a graph. Bull Math Biophys 30: 175-204.
29. Shannon CE, Weaver W (1997) The Mathematical Theory of Communication. Urbana, IL, USA: University of Illinois Press.
30. Bretscher O (2004) Linear Algebra with Applications Prentice Hall; 3rd edition.
31. Devillers J, Balaban AT (1999) Topological Indices and Related Descriptors in QSAR and QSPR. Amsterdam, The Netherlands: Gordon and Breach Science Publishers.
32. Konstantinova EV (1996) The discrimination ability of some topological and information distance indices for graphs of unbranched hexagonal systems. J Chem Inf Comput Sci 36: 54-57.
33. Konstantinova EV (2006) On some applications of information indices in chemical graph theory. In: Ahlswede R, Bäumer L, Cai N, Aydinian H, Blinovsky V, et al. (2006) General Theory of Information Transfer and Combinatorics, Springer, Lecture Notes of Computer Science. pp 831-852.
34. Todeschini R, Cazar R, Collina E (1992) The chemical meaning of topological indices. Chemometrics and Intelligent Laboratory Systems 15: 51-59.
35. Schwaighofer A, Schroeter T, Mika S, Hansen K, Laak AT, et al. (2008) A probabilistic approach to classifying metabolic stability. J Chem Inf Model 48:785-796.
36. Hansen K, Mika S, Schroeter T, Sutter A, Laak AT, et al. (2009) A benchmark data set for in silico prediction of ames mutagenicity. J Chem Inf Model.
37. Scsibrany H, Varmuza K (2004) Software SubMat. www.lcm.tuwien.ac.at. Vienna University of Technology, Institute of Chemical Engineering, Laboratory for Chemometrics, Austria.
38. Stein SE (1998) NIST, Mass spectral database 98. www.nist.gov/srd/nist1a.htm. National Institute of Standards and Technology, Gaithersburg, MD, USA.
39. (2008) R, software, a language and environment for statistical computing. www.r-project.org. R Development Core Team, Foundation for Statistical Computing, Vienna, Austria.
40. Gasteiger J, Engel T (2003) Chemoinformatics - A Textbook. Weinheim, Germany: Wiley VCH.
41. Ivanciuc O, Balaban AT (1999) The graph description of chemical structures. In: Devillers J, Balaban AT, eds. Topological Indices and Related Descriptors in QSAR and QSPAR, Gordon and Breach Science Publishers 59-167, Amsterdam, The Netherlands,.
42. Wiener H (1947) Structural determination of paraffin boiling points. Journal of the American Chemical Society 69: 17-20.
43. Randić M (1975) On characterization of molecular branching. J Amer Chem Soc 97: 6609-6615.
44. Trinajstić N (1992) Chemical Graph Theory. Boca Raton, FL, USA: CRC Press.
45. Bajorath J (2004) Chemoinformatics: Concepts, Methods, and Tools for Drug Discovery. Totowa, NJ, USA: Methods in Molecular Biology. Humana Press.
46. Basak SC (1999) Information-theoretic indices of neighborhood complexity and their applications. In: Devillers J, Balaban AT, eds. Topological Indices and Related Descriptors in QSAR and QSPAR, Gordon and Breach Science Publishers 563-595, Amsterdam, The Netherlands,.
47. Basak SC, Nikolić S, Trinajstić N, Amic D, Beslo D (2000) QSPR modeling: Graph connectivity indices versus line graph connectivity indices. J Chem Inf Comput Sci 40: 927-933.
48. Todeschini R, Consonni V, Maiocchi A (1998) The k correlation index: theory development and its applications in chemometrics. Chemometrics and Intelligent Laboratory Systems 46: 13-29.
49. Jackson B (2003) Zeros of chromatic and flow polynomials of graphs. Journal of Geometry 76: 95-109.
50. Kovše M (2009) Counting cubes in median graphs and related problems. In: Analysis of Complex Networks: From Biology to Linguistic, Wiley VCH 323-350, Weinheim, Germany,.
51. Woodall D (1992) A zero-free interval for chromatic polynomials. Discrete Mathematics 101: 333-341.
52. Bonchev D (1995) Topological order in molecules 1. molecular branching revisited. Journal of Molecular Structure: THEOCHEM 336: 137-156.