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  • 1
    Electronic Resource
    Electronic Resource
    Topological analysis of some special graphs. III. Regular polyhedra (1991)
    Springer
    Journal of cluster science 2 (1991), S. 105-116 
    Details
    ISSN: 1572-8862
    Keywords: Electronic structure ; cluster ; eigenvectors ; Kronecker product
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A regular polyhedron is isomorphic to a cluster on which every face has same number of bonds and every atom has an equal number of coordinating atoms. A general strategy for generating the eigenvectors and the eigenvalues of regular polyhedra is given. Net sign analyses are also performed on the eigenvectors of regular polyhedra. The results provide us a quick way to grasp the topological feature of the electronic structure of clusters having interesting topology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00702951
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Topological analysis of some special graphs: III. Regular polyhedra (1991)
    Springer
    Journal of cluster science 2 (1991), S. 219-229 
    Details
    ISSN: 1572-8862
    Keywords: Atomic cluster ; cluster bonding ; cluster structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A regular polyhedron is isomorphic to a cluster on which every face has same number of bonds and every atom has an equal number of coordinating atoms. A general strategy for generating the eigenvectors and the eigenvalues of regular polyhedra is given. Not sign analyses are also performed on the eigenvectors of regular polyhedra. The results provide us a quick way to grasp the topological feature of the electronic structure of clusters having interesting topology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00702829
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Topological analysis of some special classes of graphs. II. steps, ladders, cylinders (1993)
    Springer
    Journal of mathematical chemistry 14 (1993), S. 231-241 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract A general strategy is proposed for generating the eigenvectors and the eigenvalues of some special classes of graphs from the well-known chemical graphs such as lines and cycles which are isomorphic to the hydrogen-suppressed linear and cyclic polyenes. This method is applied to step graphs, ladders, cylinders, etc. Net sign analyses are then performed for all these special classes of graphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01164469
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On eigenvalues and eigenvectors of graphs (1993)
    Springer
    Journal of mathematical chemistry 12 (1993), S. 121-135 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract It is known that there exists an equivalence relation between the adjacency matrix of graph theory and the Hückel matrix of Hückel molecular orbital theory. This paper presents some useful methods which allow us to systematically find eigenvalues and eigenvectors of various classes of graphs without calculating characteristic polynomials. Results obtained from this study give insight into the topological studies of molecular orbitals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01164630
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Net signs of molecular graphs: Dependence of molecular structure (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 87-95 
    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: The concept of internal connectivity associates to each eigenvector of the molecular graph a graph with signed edges. We show that the respective edge signs can be deduced without knowing the graph eigenvectors. The dependence of the edge signs on molecular structure is elucidated. The sign of an edge whose end vertices are νr and νs is found to be the result of separate interactions through all paths connecting the vertices νr and νs. The analysis of the edge signs is particularly simple in the case of acyclic systems. © 1994 John Wiley & Sons, Inc.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560490204
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Eigenvector and eigenvalues of some special graphs. IV. Multilevel circulants (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 41 (1992), S. 105-116 
    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 multilevel circulant is defined as a graph whose adjacency matrix has a certain block decomposition into circulant matrices. A general algebraic method for finding the eigenvectors and the eigenvalues of multilevel circulants is given. Several classes of graphs, including regular polyhedra, suns, and cylinders can be analyzed using this scheme.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560410111
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    The Wiener polynomial of a graph (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 959-969 
    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: The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the elementary properties of this polynomial and compute it for some common graphs. We then find a formula for the Wiener polynomial of a dendrimer, a certain highly regular tree of interest to chemists, and show that it is unimodal. Finally, we point out a connection with the Poincaré polynomial of a finite Coxeter group. © 1996 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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