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  • 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
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 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/BF00552651
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Analysis of the π-electronic structure of infinitely large networks (1991)
    Springer
    Theoretical chemistry accounts 81 (1991), S. 105-123 
    Details
    ISSN: 1432-2234
    Keywords: Coulson's integral method ; Bond alternation ; π-Electronic structure ; Polycyclic aromatics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary Applying the Coulson and Longuet-Higgins integral method to polycyclic aromatics, the analytical solutions of bond orders, π-electronic energy and benzene character for the infinitely large cyclic polyacene and polyphenanthrene with various modes of bond alternation are obtained in the HMO scheme. Most of the results are explicitly and newly expressed in terms of three kinds of the elliptic integrals. Judging from the magnitudes of bond orders and benzene character the most probable modes of the bond alternation for these two networks are discussed with their Kekulé structures. It was shown that if bond alternation is properly taken into consideration, HMO calculation can fairly well reproduce the results obtained by more sophisticated methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01126674
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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