Review article

Mathematical Properties of Molecular Descriptors Based on Distances

Bo Zhou orcid.org/0000-0001-7321-9554 ; Department of Mathematics, South China Normal University, Guangzhou 510631, P. R. China
Nenad Trinajstić ; The Ruđer Bošković Institute, P. O. Box 180, HR-10002 Zagreb, Croatia

Abstract

A survey of a number of molecular descriptors based on distance matrices and distance eigenvalues
is given. The following distance matrices are considered: the standard distance matrix, the reverse
distance matrix, the complementary distance matrix, the resistance-distance matrix, the detour matrix, the
reciprocal distance matrix, the reciprocal reverse Wiener matrix and the reciprocal complementary distance
matrix. Mathematical properties are discussed for the following molecular descriptors with a special
emphasis on their upper and lower bounds: the reverse Wiener index, the Harary index, the reciprocal reverse
Wiener index, the reciprocal complementary Wiener index, the Kirchhoff index, the detour index,
the Balaban index, the reciprocal Balaban index, the reverse Balaban index and the largest eigenvalues of
distance matrices. This set of molecular descriptors found considerable use in QSPR and QSAR.

Keywords

Distance matrices; Wiener-like indices; distance eigenvalues; Balaban-like indices; upper and lower bounds; QSPR; QSAR

Hrčak ID:

56027

URI

https://hrcak.srce.hr/56027

Publication date:

15.7.2010.

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