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  • 1
    Electronic Resource
    Electronic Resource
    Fibonacci graphs possessing identical matching polynomials (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2396-2398 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A sequence of Fibonacci graphs is defined. A special case of Fibonacci graphs, i.e., those with identical matching polynomials, is discussed and conditions under which they appear are given. The appearance of Fibonacci graphs with identical matching polynomials may have some implications in statistical physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526827
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  • 2
    Electronic Resource
    Electronic Resource
    Note on the application of the reduced graph model in conjunction with search trees to the enumeration ofKekulé structures (1984)
    Springer
    Monatshefte für Chemie 115 (1984), S. 1299-1312 
    Details
    ISSN: 1434-4475
    Keywords: Benzenoid hydrocarbons ; Enumeration of Kekulé structures ; Reduced graph model ; Search trees
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Das Modell erlaubt mit der im Titel genannten Kombination eine neuartige Methode zur Ermittlung und Generierung vonKekulé-Strukturen. Das Verfahren ist für große benzoide Kohlenwasserstoffe geeignet, die aus cata- und (dünnen) peri-kondensierten Teilstrukturen bestehen.
    Notes: Abstract The reduced graph model, when used in conjunction with the search trees method, provides a novel combinatorial procedure for the enumeration and generation ofKekulé structures. The procedure is suited for large benzenoid hydrocarbons consisting of cata- and thin peri-condensed parts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00798307
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Characteristic polynomials of large graphs. On alternate form of characteristic polynomial [1] (1984)
    Springer
    Theoretical chemistry accounts 65 (1984), S. 191-197 
    Details
    ISSN: 1432-2234
    Keywords: Characteristic polynomial ; acyclic polynomial ; cycle polynomial
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A recursion exists between the absolute magnitudes of the coefficients of the characteristic polynomials of certain families of cyclic and acyclic graphs which makes their computation quite easy for very large graphs using a pencil-and-a-paper approach. Structural requirements are given for such families of graphs which are of interest to the problem of recognition defined in [1].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00551332
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  • 4
    Electronic Resource
    Electronic Resource
    Combinatorial Clar sextet theory (1986)
    Springer
    Theoretical chemistry accounts 70 (1986), S. 53-65 
    Details
    ISSN: 1432-2234
    Keywords: Clar sextet theory ; Benzenoid hydrocarbons ; Graph theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Clar structures recently used as basis-set to compute resonance energies [9] are identified as maximal independent sets of benzenoid hydrocarbons “colored” in a special way. Binomial properties of such objects are induced for several catafusenes and perifusenes (Eqs. 2–31). Novel polynomials, called Clar polynomials, are given for perifusens in terms of units of catafusenes which allow display and enumeration of the populations of their Clar structures. The work is particularly pertinent to that of [8] and [9].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00531152
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  • 5
    Electronic Resource
    Electronic Resource
    Applications of caterpillar trees in chemistry and physics (1987)
    Springer
    Journal of mathematical chemistry 1 (1987), S. 153-174 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The relations of caterpillar trees (which are also known as Gutman trees and benzenoid trees) to other mathematical objects such as polyhex graphs, Clar graphs, king polyominos, rook boards and Young diagrams are discussed. Potential uses of such trees in data reduction, computational graph theory, and in the ordering of graphs are considered. Combinatorial and physical properties of benzenoid hydrocarbons can be studied via related caterpillars. It thus becomes possible to study the properties of large graphs such as benzenoid (i.e. polyhex) graphs in terms of much smaller tree graphs. Generation of the cyclic structures of wreath and generalized wreath product groups through the use of caterpillar trees is illustrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01205666
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  • 6
    Electronic Resource
    Electronic Resource
    Kekulé structures as graph generators (1993)
    Springer
    Journal of mathematical chemistry 14 (1993), S. 305-318 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Kekulé valence-bond structures of catacondensed conjugated hydrocarbons with no, one, two and three branched cycles (which may be 4-, 6- and/or 8-membered) are used to generate highly regular vertex-transitive graphs through the application of an equivalence relation to the sextet of π-electrons in theterminal rings of the hydrocarbon. The partitioning of a given set of Kekulé structures allows the study of certain novel combinatorial aspects of Kekulé counts. The graph- generating character reported here is closely related to the recent work of Randić, Woodworth, Kleiner and Hosoya.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01164473
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  • 7
    Electronic Resource
    Electronic Resource
    Fibonacci numbers in the topological theory of benzenoid hydrocarbons and related graphs (1989)
    Springer
    Journal of mathematical chemistry 3 (1989), S. 1-23 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Fibonacci numbers are studied with respect to the topological theory of benzenoid hydrocarbons. These numbers are identified as the number of Kekulé structures of nonbranched all-benzenoid hydrocarbons, the number of matchings of paths, the number of independent sets of vertices of paths, the number of nonattacking rooks of certain rook boards, as well as the number of Clar structures of certain benzenoid hydrocarbons. Fibonacci numbers were also identified as the number of conjugated circuits of certain benzenoid hydrocarbons and thus they were also related to the structure-resonance model. Maximal independent sets of caterpillar trees are also shown to be Fibonacci numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01171882
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  • 8
    Electronic Resource
    Electronic Resource
    Novel graph-theoretical approach to estimating the relative importance of individual Kekulé valence structures. I. Simple catacondensed systemsThis paper is dedicated to Professor Milan Randić. (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 771-778 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A novel graph-theoretical approach for ordering Kekulé valence structures of benzenoid hydrocarbons is presented. The approach involves the transformation of the Kekulé structures into the subspaces of their individual double bonds. The submolecules generated in this way [H. Joela, Theor. Chim. Acta 39, 241 (1975)] are ordered according to suitable connectivity indices. The resulting orders parallel those predicted from the so called Kekulé indices [A. Graocvac, I. Gutman, M. Randić, and N. Trinajstć, J. Am. Chem. Soc. 95, 6267 (1973)]. A relation is thus illustrated between VB and MO theories. The method is new and allows the prediction of the relative stabilities of structures from purely combinatorial vent without resort to computer.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560210502
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  • 9
    Electronic Resource
    Electronic Resource
    Novel graph-theoretical approach to estimating the relative importance of individual Kekulé valence structures. II. Benzenoid systems having four to seven fused benzene rings: “Pseudodegenerate” statesThis paper is dedicated to Professor Milan Randić. (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 779-792 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Kekulé structures of 10 nonlinear acenes comprising 83 graphs are studied through the use of connectivities [M. Randić, J. Am. Chem. Soc. 97, 6609 (1975)] of their corresponding submolecules [H. Joela, Theor. Chim. Acta 39, 241 (1975)]. In certain rare cases states were identified to have identical branching indices but different Kekulé indices [A. Graovac, I. Gutman, M. Randić, and N. Trinajstić, J. Am. Chem. Soc. 95, 6267 (1973)]. Such states are termed pseudodegenerate states. A method is described to forecast and another to remedy such situations. The method emphasizes the relation between VB (resonance) and MO theories using graph-theoretical concepts.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560210503
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  • 10
    Electronic Resource
    Electronic Resource
    Novel graph-theoretical approach to estimating the relative importance of individual Kekulé valence structures. III. Nonalternate and nonbenzenoid hydrocarbonsThis paper is dedicated to Professor Milan Randić. (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 793-797 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Molecular connectivities of submolecules [H. Joela, Theor. Chim. Acta 39, 241 (1975)] corresponding to Kekulé structures of nine nonalternate hydrocarbons and four nonbenzenoid hydrocarbons containing four-membered rings are correlated with their Kekulé indices. In the latter class of compounds it was observed that the corresponding submolecules contain cut vertices and bridges in contrast to submolecules of benzenoid hydrocarbons which are devoid of such bridges. It was observed, furthermore, that the branching index goes up with the number of bridges in the submolecule. The results present an application to the abstract relation [D. Cvetković, I. Gutman, and N. Trinajstić, J. Chem. Phys. 61, 2700 (1974)] between resonance and MO theories.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560210504
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