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  • 1
    Electronic Resource
    Electronic Resource
    Kekulé structure counts: General formulations for primitive coronoid hydrocarbons (1991)
    Springer
    Monatshefte für Chemie 122 (1991), S. 435-444 
    Details
    ISSN: 1434-4475
    Keywords: Kekulé structure ; Coronoid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Es werden Kekulé-Strukturzählungen (K) für einfache Coronoide behandelt. Die Formel fürK wird durch neugefundene Eigenschaften ergänzt. So wird eine Art von Symmetrie in den mathematischen Formulierungen erreicht. Eine andere generelle Formulierung derK-Zahlen wird in Form von Polynomen bereitgestellt, welche aus uneinsichtigen Gründen als die passenden Polynome von Cyclen identifiziert wurden.
    Notes: Summary The Kekulé structure counts (K) for primitive coronoids are treated. TheK formula which involves the trace of a matrix product is recalled and supplemented with new findings. In this way a kind of symmetry in the mathematical formulations is restored. Another general formulation for theK number is provided in terms of polynomials which, for a somewhat mysterious reason, are identified as the matching polynomials of cycles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00809795
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    Paper (German National Licenses)
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  • 2
    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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    Paper (German National Licenses)
    Fulltext
  • 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
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Topological dependency of the aromatic sextets in polycyclic benzenoid hydrocarbons. Recursive relations of the sextet polynomial (1983)
    Springer
    Theoretical chemistry accounts 64 (1983), S. 153-170 
    Details
    ISSN: 1432-2234
    Keywords: Polycyclic benzenoid hydrocarbon ; Kekulé structure ; Clar's aromatic sextet ; Sextet polynomial ; Graph theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Mathematical meaning of the Clar's “aromatic sextet” is clarified by analysing the topological dependency of the sextet polynomial. Generalised recursive method for obtaining the sextet polynomial of a polyhex graph is presented. It is shown that the concept of the “super sextet” is necessarily introduced, if one-to-one correspondence between the Kekulé and sextet patterns is assumed. Topological dependency of the maximum number of resonant sextets is clarified and discussed in relation to the aromaticity and stability of polycyclic benzenoid hydrocarbons.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00551393
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    Paper (German National Licenses)
    Fulltext
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