Mathematical Properties of Molecular Descriptors Based on Distances

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