메뉴 건너뛰기




Volumn 40, Issue , 1999, Pages 187-201

On the complexity of molecular graphs

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0011923640     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (18)

References (50)
  • 1
    • 0004132817 scopus 로고
    • Touchstone/Simon&Schuster, New York
    • M.Mitchell Waldrop, Complexity, Touchstone/Simon&Schuster, New York, 1992.
    • (1992) Complexity
    • Waldrop, M.M.1
  • 2
    • 0038893441 scopus 로고    scopus 로고
    • The latest C-theory
    • C-theories are cybernetics (appearing in the 1960s), catastrophe theory (appearing in the 1970s) and the chaos theory (appearing in the 1980s)
    • S.H. Strogatz, The Latest C-Theory, Nature 387, 771-772 (1997); C-theories are cybernetics (appearing in the 1960s), catastrophe theory (appearing in the 1970s) and the chaos theory (appearing in the 1980s).
    • (1997) Nature , vol.387 , pp. 771-772
    • Strogatz, S.H.1
  • 6
    • 0004255608 scopus 로고
    • Alfred A. Knopf, Inc., New York
    • M. Crichton, The Lost World, Alfred A. Knopf, Inc., New York, 1995, p. 3. This is a sequel to the bestselling novel of the same author "Jurassic Park" (Alfred A. Knopf, Inc., New York, 1990), which was inspired by Sir Arthur Conan Doyle's novel of the same title.
    • (1995) The Lost World , pp. 3
    • Crichton, M.1
  • 7
    • 0003847310 scopus 로고
    • Harvard University Press, Cambridge, MA
    • G. Birkhoff, Aesthetic Measure, Harvard University Press, Cambridge, MA, 1933.
    • (1933) Aesthetic Measure
    • Birkhoff, G.1
  • 11
    • 0002164238 scopus 로고    scopus 로고
    • Are the concepts of chemistry all fuzzy?
    • D.H. Rouvray, Ed., Wiley, New York
    • D.H. Rouvray, Are the Concepts of Chemistry all Fuzzy?, in: Concepts in Chemistry - A Contemporary Challenge, D.H. Rouvray, Ed., Wiley, New York, 1997, pp. 1-15
    • (1997) Concepts in Chemistry - A Contemporary Challenge , pp. 1-15
    • Rouvray, D.H.1
  • 13
    • 0343071989 scopus 로고
    • Information theory, distance matrix and molecular branching
    • D. Bonchev and N. Trinajstić, Information Theory, Distance Matrix and Molecular Branching, J. Chem. Phys. 67, 4517-4533 (1977).
    • (1977) J. Chem. Phys. , vol.67 , pp. 4517-4533
    • Bonchev, D.1    Trinajstić, N.2
  • 15
    • 0000524226 scopus 로고
    • The first general index of molecular complexity
    • S.H. Bertz, The First General Index of Molecular Complexity, J. Am. Chem. Soc. 103, 3599-3601 (1981).
    • (1981) J. Am. Chem. Soc. , vol.103 , pp. 3599-3601
    • Bertz, S.H.1
  • 16
    • 0000918669 scopus 로고
    • Convergence, molecular complexity and synthetic analysis
    • S.H. Bertz, Convergence, Molecular Complexity and Synthetic Analysis, J. Am. Chem. Soc. 104, 5801-580/3 (1982).
    • (1982) J. Am. Chem. Soc. , vol.104 , pp. 5801-5803
    • Bertz, S.H.1
  • 17
    • 0002183826 scopus 로고
    • On the complexity of graphs and molecules
    • S.H. Bertz, On the Complexity of Graphs and Molecules, Bull. Math. Biol. 45, 849-855 (1983).
    • (1983) Bull. Math. Biol. , vol.45 , pp. 849-855
    • Bertz, S.H.1
  • 18
    • 0001787983 scopus 로고
    • A mathematical model of molecular complexity
    • R.B. King, Ed., Elsevier, Amsterdam
    • S.H. Bertz, A Mathematical Model of Molecular Complexity, in: Chemical Applications of Topology and Graph Theory, R.B. King, Ed., Elsevier, Amsterdam, 1983, pp. 206-221 ; see also E de Bono, Simplicity, Viking, London, 1998.
    • (1983) Chemical Applications of Topology and Graph Theory , pp. 206-221
    • Bertz, S.H.1
  • 19
    • 0006074517 scopus 로고    scopus 로고
    • Viking, London
    • S.H. Bertz, A Mathematical Model of Molecular Complexity, in: Chemical Applications of Topology and Graph Theory, R.B. King, Ed., Elsevier, Amsterdam, 1983, pp. 206-221 ; see also E de Bono, Simplicity, Viking, London, 1998.
    • (1998) Simplicity
    • De Bono, E.1
  • 20
    • 0000520634 scopus 로고
    • Structural complexity and molecular properties of cyclic systems with acyclic branches
    • O. Mekenyan, D. Bonchev and N. Trinajstić, Structural Complexity and Molecular Properties of Cyclic Systems with Acyclic Branches, Croat. Chem. Acta 56, 237-261 (1983).
    • (1983) Croat. Chem. Acta , vol.56 , pp. 237-261
    • Mekenyan, O.1    Bonchev, D.2    Trinajstić, N.3
  • 21
    • 0001588769 scopus 로고
    • On the topological complexity of chemical systems
    • R.B. King and D.H. Rouvray, Eds., Elsevier, Amsterdam
    • D. Bonchev and O.E. Polansky, On the Topological Complexity of Chemical Systems, in: Graph Theory and Topology in Chemistry, R.B. King and D.H. Rouvray, Eds., Elsevier, Amsterdam, 1987, pp. 126-158.
    • (1987) Graph Theory and Topology in Chemistry , pp. 126-158
    • Bonchev, D.1    Polansky, O.E.2
  • 22
    • 0023202542 scopus 로고    scopus 로고
    • Use of molecular complexity indices in predictive pharmacology and toxicology: A QSAR approach
    • 19887
    • S.C. Basak, Use of Molecular Complexity Indices in Predictive Pharmacology and Toxicology: A QSAR Approach, Med. Sci. Res. 15, 605-609 (19887).
    • Med. Sci. Res. , vol.15 , pp. 605-609
    • Basak, S.C.1
  • 23
    • 0011416646 scopus 로고
    • A complexity measure for chemical compounds
    • B.L. Mil'man, A Complexity Measure for Chemical Compounds, J. Struct. Chem. 29, 957-960 (1988).
    • (1988) J. Struct. Chem. , vol.29 , pp. 957-960
    • Mil'man, B.L.1
  • 24
    • 0028674316 scopus 로고
    • Complexity and emergence in drug research
    • L.B. Kier and B. Testa, Complexity and Emergence in Drug Research, Adv. Drug Res. 26, 1-43 (1995)
    • (1995) Adv. Drug Res. , vol.26 , pp. 1-43
    • Kier, L.B.1    Testa, B.2
  • 27
  • 28
    • 0002398590 scopus 로고    scopus 로고
    • Novel indices for the topological complexity of molecules
    • D. Bonchev, Novel Indices for the Topological Complexity of Molecules, SAR QSAR Environ. Res. 7, 23-43 (1997).
    • (1997) SAR QSAR Environ. Res. , vol.7 , pp. 23-43
    • Bonchev, D.1
  • 30
    • 0040671470 scopus 로고
    • Life, information theory and topology
    • N. Rashevsky, Life, Information Theory and Topology, Bull. Math.Biophys. 27, 379-423 (1955).
    • (1955) Bull. Math.Biophys. , vol.27 , pp. 379-423
    • Rashevsky, N.1
  • 31
    • 0001664648 scopus 로고
    • On the number of spanning trees in a molecular graph
    • R.B. Mallion, On the Number of Spanning Trees in a Molecular Graph, Chem. Phys. Lett. 36, 170-174 (1975).
    • (1975) Chem. Phys. Lett. , vol.36 , pp. 170-174
    • Mallion, R.B.1
  • 32
    • 0011561063 scopus 로고
    • Counting the spanning trees of a labelled molecular-graph
    • I. Gutman, R.B. Mallion and J.W.Essam, Counting the Spanning Trees of a Labelled Molecular-Graph, Mol. Phys. 50, 859-877 (1983).
    • (1983) Mol. Phys. , vol.50 , pp. 859-877
    • Gutman, I.1    Mallion, R.B.2    Essam, J.W.3
  • 33
    • 3042796374 scopus 로고
    • Counting the spanning trees of labelled, planar molecular graphs embedded on the surface on a sphere
    • R.B. King and D.H. Rouvray, Eds., Elsevier, Amsterdam
    • B. O'Leary and R.B. Mallion, Counting the Spanning Trees of Labelled, Planar Molecular Graphs Embedded on the Surface on a Sphere, in: Graph Theory and Topology in Chemistry, R.B. King and D.H. Rouvray, Eds., Elsevier, Amsterdam, 1987, pp. 544-551.
    • (1987) Graph Theory and Topology in Chemistry , pp. 544-551
    • O'Leary, B.1    Mallion, R.B.2
  • 34
    • 0011627435 scopus 로고
    • Some graph-theoretical aspects of simple "ring-current" calculations on conjugated systems
    • R.B. Mallion, Some Graph-theoretical Aspects of Simple "Ring-Current" Calculations on Conjugated Systems, Proc. Roy. Soc. (London) A341, 429-449 (1975).
    • (1975) Proc. Roy. Soc. (London) , vol.A341 , pp. 429-449
    • Mallion, R.B.1
  • 35
    • 49249150528 scopus 로고
    • Ring current theories in nuclear magnetic resonance
    • J.W. Emsley, J. Feeney and L.H. Sutcliffe, Eds., Pergamon Press, Oxford
    • C.W. Haig and R.B. Mallion, Ring Current Theories in Nuclear Magnetic Resonance, in: Progress in Nuclear Magnetic Resonance Spectroscopy, J.W. Emsley, J. Feeney and L.H. Sutcliffe, Eds., Pergamon Press, Oxford, 1979/1980, Vol.-13, pp. 303-344.
    • (1979) Progress in Nuclear Magnetic Resonance Spectroscopy , vol.13 , pp. 303-344
    • Haig, C.W.1    Mallion, R.B.2
  • 36
    • 0011689179 scopus 로고
    • Rationalisation of relative "ring-current" sizes in polycyclic conjugated hydrocarbons
    • C.W. Haig and R.B. Mallion, Rationalisation of Relative "Ring-Current" Sizes in Polycyclic Conjugated Hydrocarbons, Croat. Chem. Acta 62, 1-26 (1989).
    • (1989) Croat. Chem. Acta , vol.62 , pp. 1-26
    • Haig, C.W.1    Mallion, R.B.2
  • 38
    • 0141979985 scopus 로고
    • Ring currents and proton magnetic resonance in aromatic molecules
    • R. McWeeny, Ring Currents and Proton Magnetic Resonance in Aromatic Molecules, Mol. Phys. 1, 311-321 (1958).
    • (1958) Mol. Phys. , vol.1 , pp. 311-321
    • McWeeny, R.1
  • 39
    • 0039486131 scopus 로고
    • Laplacian matrices of graphs
    • A. Graovac, Ed., Elsevier, Amsterdam
    • B. Mohar, Laplacian Matrices of Graphs, in: MATH/CHEM/COMP 1988, A. Graovac, Ed., Elsevier, Amsterdam, 1989, pp. 1-8.
    • (1989) MATH/CHEM/COMP 1988 , pp. 1-8
    • Mohar, B.1
  • 42
    • 0002398590 scopus 로고    scopus 로고
    • Novel indices for the topological complexity of molecules
    • D. Bonchev, Novel Indices for the Topological Complexity of Molecules, SAR QSAR Environ. Res. 7, 23-43 (1997).
    • (1997) SAR QSAR Environ. Res. , vol.7 , pp. 23-43
    • Bonchev, D.1
  • 44
    • 0038893439 scopus 로고    scopus 로고
    • S. Bertz, e-mail of March 16th, 1999
    • S. Bertz, e-mail of March 16th, 1999.
  • 45
    • 3042712352 scopus 로고
    • An algorithmic approach to the number of spanning trees in buckminsterfullerene
    • Erratum: ibid. 16, 389-390 (1994)
    • P.E. John and R.B. Mallion, An Algorithmic Approach to the Number of Spanning Trees in Buckminsterfullerene, J. Math. Chem. 15, 261-271 (1994); Erratum: ibid. 16, 389-390 (1994).
    • (1994) J. Math. Chem. , vol.15 , pp. 261-271
    • John, P.E.1    Mallion, R.B.2
  • 46
    • 0027929267 scopus 로고
    • On the number of spanning trees in fullerenes
    • Z. Mihalić and N. Trinajstić, On the Number of Spanning Trees in Fullerenes, Fullerene Sci. Technol. 2, 89-95 (1994).
    • (1994) Fullerene Sci. Technol. , vol.2 , pp. 89-95
    • Mihalić, Z.1    Trinajstić, N.2
  • 48
    • 0041037845 scopus 로고    scopus 로고
    • On topological indices, boiling points and cycloalkanes
    • in press
    • While this manuscript was submitted, refereed and revised, Rücker and Rücker (e.g., G. Rücker and C. Rücker, On Topological Indices, Boiling Points and Cycloalkanes, J. Chem. Inf. Comput. Sci., in press; Walk Counts, Labyrinthicity and Complexity of Acyclic and Cyclic Graphs and Molecules, J. Chem. Inf. Comput. Sci., in press) advocated the use of the total walk count (twc) as a molecular complexity measure. These authors claim that twc is easy to compute (e.g., G. Rücker and C. Rücker, Counts of All Walks as Atomic and Molecular Descriptors, J. Chem. Inf. Comput. Sci. 33, 683-695 (1993)) and is dependent on size, branching, cyclicity, symmetry, heteroatoms and heterobonds.
    • J. Chem. Inf. Comput. Sci.
    • Rücker, G.1    Rücker, C.2
  • 49
    • 0027658970 scopus 로고    scopus 로고
    • Walk counts, labyrinthicity and complexity of acyclic and cyclic graphs and molecules
    • in press
    • While this manuscript was submitted, refereed and revised, Rücker and Rücker (e.g., G. Rücker and C. Rücker, On Topological Indices, Boiling Points and Cycloalkanes, J. Chem. Inf. Comput. Sci., in press; Walk Counts, Labyrinthicity and Complexity of Acyclic and Cyclic Graphs and Molecules, J. Chem. Inf. Comput. Sci., in press) advocated the use of the total walk count (twc) as a molecular complexity measure. These authors claim that twc is easy to compute (e.g., G. Rücker and C. Rücker, Counts of All Walks as Atomic and Molecular Descriptors, J. Chem. Inf. Comput. Sci. 33, 683-695 (1993)) and is dependent on size, branching, cyclicity, symmetry, heteroatoms and heterobonds.
    • J. Chem. Inf. Comput. Sci.
  • 50
    • 0027658970 scopus 로고    scopus 로고
    • Counts of all walks as atomic and molecular descriptors
    • While this manuscript was submitted, refereed and revised, Rücker and Rücker (e.g., G. Rücker and C. Rücker, On Topological Indices, Boiling Points and Cycloalkanes, J. Chem. Inf. Comput. Sci., in press; Walk Counts, Labyrinthicity and Complexity of Acyclic and Cyclic Graphs and Molecules, J. Chem. Inf. Comput. Sci., in press) advocated the use of the total walk count (twc) as a molecular complexity measure. These authors claim that twc is easy to compute (e.g., G. Rücker and C. Rücker, Counts of All Walks as Atomic and Molecular Descriptors, J. Chem. Inf. Comput. Sci. 33, 683-695 (1993)) and is dependent on size, branching, cyclicity, symmetry, heteroatoms and heterobonds.
    • (1993) J. Chem. Inf. Comput. Sci. , vol.33 , pp. 683-695
    • Rücker, G.1    Rücker, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.