Atomic branching in molecules

Authors

  • Ernesto Estrada,

    Corresponding author
    1. Complex Systems Research Group, X-Rays Unit, RIAIDT, Edificio CACTUS, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
    • Complex Systems Research Group, X-Rays Unit, RIAIDT, Edificio CACTUS, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
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  • Juan A. Rodríguez-Velázquez,

    1. Department of Mathematics, University Carlos III de Madrid, 28911 Leganés, Madrid, Spain
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  • Milan Randić

    1. Complex Systems Research Group, X-Rays Unit, RIAIDT, Edificio CACTUS, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
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Abstract

A graph theoretic measure of extended atomic branching is defined that accounts for the effects of all atoms in the molecule, giving higher weight to the nearest neighbors. It is based on the counting of all substructures in which an atom takes part in a molecule. We prove a theorem that permits the exact calculation of this measure based on the eigenvalues and eigenvectors of the adjacency matrix of the graph representing a molecule. The definition of this measure within the context of the Hückel molecular orbital (HMO) and its calculation for benzenoid hydrocarbons are also studied. We show that the extended atomic branching can be defined using any real symmetric matrix, as well as any Hermitian (self-adjoint) matrix, which permits its calculation in topological, geometrical, and quantum chemical contexts. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

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