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  • 1
    Electronic Resource
    Electronic Resource
    On the calculation of the acyclic polynomial (1978)
    Springer
    Theoretical chemistry accounts 48 (1978), S. 279-286 
    Details
    ISSN: 1432-2234
    Keywords: Acyclic polynomial ; Graph theory ; Topological index
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Graphical methods are developed for recursive evaluation of the acyclic polynomial. Analytical formulas of the acyclic polynomials for several specific series of graphs are given. Mathematical properties of the derivatives of the acyclic polynomial are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00552656
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    On the calculation of the acyclic polynomial (1978)
    Springer
    Theoretical chemistry accounts 48 (1978), S. 279-286 
    Details
    ISSN: 1432-2234
    Keywords: Acyclic polynomial ; Graph theory ; Topological index
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Graphical methods are developed for recursive evaluation of the acyclic polynomial. Analytical formulas of the acyclic polynomials for several specific series of graphs are given. Mathematical properties of the derivatives of the acyclic polynomial are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02394586
    Library Location Call Number Volume/Issue/Year Availability
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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/BF02394808
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    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Exact dimer statistics and characteristic polynomials of cacti lattices (1989)
    Springer
    Theoretical chemistry accounts 76 (1989), S. 315-329 
    Details
    ISSN: 1432-2234
    Keywords: Cacti lattices ; Dimer statistics ; Graph theory ; Characteristic polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The pruning method developed earlier by one of the authors (K.B.) combined with the operator method is shown to yield powerful recursive relations for generating functions for dimer statistics and characteristic polynomials of cacti graphs and cacti lattices. The method developed is applied to linear cacti, Bethe cacti of any length containing rings of any size, and cyclic cacti of any length and size. It is shown that exact dimer statistics can be done on any cactus lattice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00529932
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    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Stability of small fullerenes C n (n=36,40 and 60): A topological and molecular orbital approach (1995)
    Springer
    Theoretical chemistry accounts 90 (1995), S. 75-86 
    Details
    ISSN: 1432-2234
    Keywords: Stability of fullerenes ; AM1 method ; Topological parameters ; Fused 5-membered rings ; Abutting bond
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary By semi-empirical molecular orbital calculations stability of fullerenes was analyzed in terms of topological parameters, such as the number of special fragments and the number of three types of abutting bonds between two 5-membered rings. Relative stability was compared by AM1 method for all spectrally distinct closed-shell isomers of C36 and C40 fullerenes, and for some closed-shell isomers of C60 fullerene. Molecular geometries of these fullerenes were also optimized. Their relative stabilities were well explained by the instability of abutting bonds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01113841
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    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    A topological index for the totalπ-electron energy (1975)
    Springer
    Theoretical chemistry accounts 38 (1975), S. 37-47 
    Details
    ISSN: 1432-2234
    Keywords: Graph theory ; Topological studies in organic chemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A modified topological index $$\tilde Z_G $$ is proposed to be defined as $$\tilde Z_G = \sum\limits_{k = 0}^{[N/2]} {( - 1)^k } a_{2k} $$ for characterising theπ-electronic system of a conjugated hydrocarbonG withN carbon atoms, wherea 2k is the coefficient of the characteristic polynomial ofG defined as $$P_G (X) = ( - 1)^N \det |A - XE| = \sum\limits_{k = 0}^N { a_k X^{N - k} } $$ with an adjacency matrixA and the unit matrixE. $$\tilde Z_G $$ is identical toZ G for a tree graph, or a chain hydrocarbon.Z G increases with a (4n+2)-membered ring formation and decreases with a 4n-membered ring formation. The totalπ-electron energyE π of the Hückel molecular orbital is shown to be related with $$\tilde Z_G $$ asE π =Cln $$\tilde Z_G $$ . With this relation generalised and extended Hückel rules for predicting the stability of an arbitrary network are proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01046555
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 7
    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
  • 8
    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
  • 9
    Electronic Resource
    Electronic Resource
    Stability of small fullerenes Cn (n=36, 40 and 60): A topological and molecular orbital approach (1995)
    Springer
    Theoretica chimica acta 90 (1995), S. 75-86 
    Details
    ISSN: 0040-5744
    Keywords: Key words: Stability of fullerenes ; AM1 method ; Topological parameters ; Fused 5-membered rings ; Abutting bond
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary.  By semi-empirical molecular orbital calculations stability of fullerenes was analyzed in terms of topological parameters, such as the number of special fragments and the number of three types of abutting bonds between two 5-membered rings. Relative stability was compared by AM1 method for all spectrally distinct closed-shell isomers of C36 and C40 fullerenes, and for some closed-shell isomers of C60 fullerene. Molecular geometries of these fullerenes were also optimized. Their relative stabilities were well explained by the instability of abutting bonds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01113841
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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