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  • Computational Chemistry and Molecular Modeling  (35)
  • Structure factor  (2)
  • Characteristic polynomial-Graph isomorphism  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Analysis of the topological dependency of the characteristic polynomial in its chebyshev expansion (1983)
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    Details
    ISSN: 1432-2234
    Keywords: Characteristic polynomial ; Chebyshev polynomial ; Topological index ; Structure factor ; Graph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The structural dependency (effect of branching and cyclisation) of an alternative form, the Chebyshev expansion, for the characteristic polynomial were investigated systematically. Closed forms of the Chebyshev expansion for an arbitrary star graph and a bicentric tree graph were obtained in terms of the “structure factor” expressed as the linear combination of the “step-down operator”. Several theorems were also derived for non-tree graphs. Usefulness and effectiveness of the Chebyshev expansion are illustrated with a number of examples. Relation with the topological index (Z G ) was discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02394808
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  • 2
    Electronic Resource
    Electronic Resource
    On alternative form of the characteristic polynomial and the problem of graph recognition (1983)
    Springer
    Theoretical chemistry accounts 62 (1983), S. 485-498 
    Details
    ISSN: 1432-2234
    Keywords: Characteristic polynomial-Graph isomorphism ; Isospectral graphs ; Graph recognition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The characteristic polynomial of a structure (molecule or a graph) is usually expressed as a function ofx. Here we explore an alternative representation of characteristic polynomials expressed in terms ofL n , the characteristic polynomials of linear chains havingn atoms. While the new forms of the characteristic polynomials are mathematically equivalent to the old forms, they appear to reflect selected structural similarities among homologous molecules better. Besides arriving at general expressions for the form of the characteristic polynomials for numerous families of compounds previously unavailable, the approach is of some interest for the old problem of graph isomorphism and graph recognition in cases of structures which can be associated with a homologous series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00557925
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Analysis of the topological dependency of the characteristic polynomial in its chebyshev expansion (1983)
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    Details
    ISSN: 1432-2234
    Keywords: Characteristic polynomial ; Chebyshev polynomial ; Topological index ; Structure factor ; Graph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The structural dependency (effect of branching and cyclisation) of an alternative form, the Chebyshev expansion, for the characteristic polynomial were investigated systematically. Closed forms of the Chebyshev expansion for an arbitrary star graph and a bicentric tree graph were obtained in terms of the “structure factor” expressed as the linear combination of the “step-down operator”. Several theorems were also derived for non-tree graphs. Usefulness and effectiveness of the Chebyshev expansion are illustrated with a number of examples. Relation with the topological index (Z G ) was discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00552651
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    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Hybridization by the maximum overlap methodSupported in part by the National Science Foundation (Grant GP-31373 and 14012X). (1974)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 643-676 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A brief survey of the maximum overlap method is presented and some computational aspects of the approach are discussed. The hybrid compositions and bond overlaps are reported for some thirty small ring compounds and a list of characteristic hybrids for various structural environments is given. The table of characteristic hybrids is extended to acyclic hydrocarbons and the transferability of the maximum overlap hybrids is demonstrated. Those aspects of the method which depend on geometrical properties of molecules have been considered in some details and the discussion is extended to some structural features of cyclic systems. In particular the asymmetry of bonds of spiro carbon atom is examined and rationalization of puckering of large macrocyclic systems is presented. In the summary it is pointed to the method and its potential to discuss structural aspects of molecules at the particular level of accuracy expected to be of great use in organic and physical organic chemistry. Further development and improvement of the method is mentioned, but already in the present form it can produce hybrids which may constitute a useful basis for other more ambitious semiempirical calculations.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560080503
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  • 5
    Electronic Resource
    Electronic Resource
    Resonance energy of very large benzenoid hydrocarbonsThis paper is dedicated to Professor Linus Pauling. (1980)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 17 (1980), S. 549-586 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The resonance energy of conjugated benzenoid systems is expressed as contributions arising from independent conjugated circuits. The scheme has been applied to numerous very large conjugated systems. In many cases, it was possible to find regularities in the increments for the resonance energy within a family of benzenoid systems as the number of benzene rings is increased.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560170314
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  • 6
    Electronic Resource
    Electronic Resource
    The graph center concept for polycyclic graphsDedicated of Professor Oscar E. Polansky for his enthusiastic support, participation, and promotion of chemical graph theory at the times when such an understanding is decisive. (1981)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 19 (1981), S. 61-82 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: While the concept of the graph center is unambiguous (and quite old) in the case of acyclic graphs, an attempt has been made recently to extend the concept to polycyclic structures using the distance matrix of a graph as the basis. In this work we continue exploring such generalizations considering in addition to the distance matrix, self-avoiding walks or paths as graph invariants of potential interest for discriminating distinctive vertex environments in a graph of polycyclic structures. A hierachy of criteria is suggested that offers a systematic approach to the vertex discrimination and eventually establishes in most cases the graph center as a single vertex, a single bond (edge), or a single group of equivalent vertices. Some applications and the significance of the concept of the graph center are presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560190107
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  • 7
    Electronic Resource
    Electronic Resource
    The graph center concept for polycyclic graphs (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 441-441 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560220221
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  • 8
    Electronic Resource
    Electronic Resource
    Unusual random walks (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 24 (1983), S. 435-452 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For most structures (molecules, graphs, lattices) a count of random walks for nonequivalent sites will give different numbers, particularly for walks of many steps. Occasionally one finds the same count of walks for nonequivalent sites. These have been termed “unusual walks” and have been closely examined in the case of trivalent graphs. While it remains to be understood what structural factors are critical, some regularities have been observed and are discussed. Unusual walks within a single structure signal “isospectural” points in a graph. A number of structures possessing unusual walks have been displayed, and a few constructive steps which do not alter the “unusual” characteristics of selected vertices have been indicated.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560240503
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  • 9
    Electronic Resource
    Electronic Resource
    A rational selection of graph-theoretical indices in the QSAR (1988)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 34 (1988), S. 267-285 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper we have addressed an important problem: how to develop a strategy for identification of the topological indices which are most important in establishing a model for structure-activity analysis. In particular we consider a rational selection of graph theoretical (topological) indices in QSAR. The approach is illustrated by the study of the toxicity of ethers on mice. The indices examined include the connectivity indices based on adjacency matrix, the conceptually related graph distance indices, and an information theoretic index based on partitioning of electrons in various domains. We have outlined the similarities and differences and discuss advantages and limitations among different approaches. Our emphasis is on the problem how to select in a rational way appropriate graph-theoretical descriptors and how to introduce higher “corrections” in order to improve derived correlation.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560340724
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  • 10
    Electronic Resource
    Electronic Resource
    On the difference in bond orders between HMO and PPP methods (1990)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 37 (1990), S. 437-448 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have examined variations in bond orders in conjugated hydrocarbons that follow improvement in MO calculations on going from topological Hückel MO to self-consistent Pariser-Parr-Pople-type calculations. Differences in individual bond orders can be interpreted as pointing to increased weights of selected Kekulé valence structures. Significantly, so indicated valence structures are those with the largest number of formal Kekulé benzene rings or the largest contribution to molecular resonance energy in terms of conjugated circuits.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560370414
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