Novel shape descriptors for molecular graphs

We report on novel graph theoretical indices which are sensitive to the sha pes of molecular graphs. In contrast to the Kier's kappa shape indices whic h were based on a comparison of a molecular graph with graphs representing the extreme shapes, the linear graph and the "star" graph, the new shape in dices are obtained by considering for all atoms the number of paths and the number of walks within a graph and then making the quotients of the number of paths and the number of walks the same length. The new shape indices sh ow much higher discrimination among isomers when compared to the kappa shap e indices. We report the new shape indices for smaller alkanes and several cyclic structures and illustrate their use in structure-property correlatio ns. The new indices offer regressions of high quality for diverse physicoch emical properties of octanes. They also have lead to a novel classification of physicochemical properties of alkanes.