Reverse Wiener indices

By subtracting from the graph diameter all topological distances one obtain s a new symmetrical matrix, reverse Wiener RW, with zeroes on the main diag onal, whose sums over rows or columns give rise to new integer-number graph invariants sigma (i) whose half-sum is a novel topological index (TI), the reverse Wiener index Lambda. Analytical forms for values of sigma (i) and Lambda of several classes of graphs are presented. Relationships with other TIs are discussed. Unlike distance sums, sigma (i) values increase from th e periphery towards the center of the graph, and they are equal to the grap h vertex degrees when the diameter of the graph is equal to 2. Structural d escriptors computed from the reverse Wiener matrix were tested in a large n umber of quantitative structure-property relationship models, demonstrating the usefulness of the new molecular matrix.