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  • Chebyshev polynomial  (2)
  • Characteristic polynomial-Graph isomorphism  (1)
  • Chemical graph theory  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    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
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 73 (1988), S. 233-246 
    ISSN: 1432-2234
    Keywords: Chemical graph theory ; Composition ; Alkanes ; Molecular chemical shift
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: 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.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 62 (1983), S. 485-498 
    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
    Library Location Call Number Volume/Issue/Year Availability
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
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