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The distance matrix in chemistry

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Abstract

The graph-theoretical (topological) distance matrix and the geometric (topographic) distance matrix and their invariants (polynomials, spectra, determinants and Wiener numbers) are presented. Methods of computing these quantities are discussed. The uses of the distance matrix in both forms and the related invariants in chemistry are surveyed. Special attention is paid to the 2D and 3D Wiener numbers, defined respectively as one half of the sum of entries in the topological distance matrix and the topographic distance matrix. These numbers appear to be very valuable molecular descriptors in the structure property correlations.

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Authors and Affiliations

  1. The Faculty of Science and Mathematics, The University of Zagreb, 41000, Zagreb, The Republic of Croatia

    Zlatko Mihalić & Darko Veljan

  2. The Faculty of Agriculture, The University of Osijek, 54001, Osijek, The Republic of Croatia

    Dragan Amić

  3. The Rugjer Bošković Institute, 41001, Zagreb, The Republic of Croatia

    Sonja Nikolić, Dejan Plavšić & Nenad Trinajstić

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  1. Zlatko Mihalić
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  2. Darko Veljan
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  4. Sonja Nikolić
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  5. Dejan Plavšić
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Dedicated to Professor Vladimir Prelog (Zurich) on the happy occasion of his 85th birthday.

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Mihalić, Z., Veljan, D., Amić, D. et al. The distance matrix in chemistry. J Math Chem 11, 223–258 (1992). https://doi.org/10.1007/BF01164206

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