Design of topological indices. Part 17 - The Szeged operator as a source of new structural descriptors

The Wiener index, equal to the sum of the molecular graph distances, is a w idely used chemical descriptor for structure-property and structure-activit y models. The Szeged index was introduced as an alternative to the Wiener i ndex for cyclic molecular graphs; for acyclic graphs the two indices have i dentical values. We define a new family of topological indices based on gra ph distances, the Szeged operator, offering a class of flexible structural descriptors. The Szeged operator computes vertex contributions by applying a function to a subset of vertices from the molecular graph; each vertex is characterized by a local invariant, such as the degree, distance sumo or r eciprocal distance sum. The structural descriptors computed with the Szeged operator are tested in a structure-property study that models the boiling temperature of 134 alkanes.