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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    ISSN: 1432-2234
    Schlagwort(e): Characteristic polynomial ; Chebyshev polynomial ; Topological index ; Structure factor ; Graph
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 73 (1988), S. 233-246 
    ISSN: 1432-2234
    Schlagwort(e): Chemical graph theory ; Composition ; Alkanes ; Molecular chemical shift
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Abstract The concept of composition as the counterpart to partition is introduced and advocated for the discussion of molecular properties. In the partition approach an observable (experimental) quantity is fragmented into contributions which are non-observable but which hopefully maintain constancy for fragments (bonds) in similar environments and thus facilitate comparison of data. With the composition as an approach the role of “fragments” and “whole” are reversed: one starts with a collection of observable fragment properties (e.g., atomic chemical shifts of NMR spectra) and then constructs an abstract non-observable quantity representing the collection of fragments as a “whole”. If a so-derived quantity for different molecules shows some regularity, the initial loss of information in condensation of independent fragment data is compensated by insight into novel structural correlations. The approach is illustrated first by ordering isomers (e.g., nonanes C9H20) with respect to their content of special graph invariants p 2 and p 3 (numbers of paths of length two and length three, respectively) and then showing that the constructed global quantity derived from individual carbon-13 NMR chemical shifts shows a regular variation with p 2 and p 3, very similar to isomeric variations of numerous thermodynamic properties of nonanes. Subsequently it is outlined how the difference (p 2 p 3) leads to a correlation for mean carbon-13 chemical shifts in octanes and nonanes, taken as an illustration for the approach. It is expected that the outlined approach opens new avenues for data reduction and the search for structure-property correlations.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    ISSN: 1432-2234
    Schlagwort(e): Characteristic polynomial ; Chebyshev polynomial ; Topological index ; Structure factor ; Graph
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
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