Potential application of novel AL-indices as molecular descriptors

A topological index or a descriptor is a graph invariant that describes the structure of a graph as a numerical value. This paper proposes eight novel indices called AL-indices, based on distance and degree, and analyzes their behavior to show that they can serve as potentially useful molecular descriptors. We find that among the proposed indices many have very good discriminative power when compared to the existing vertex-degree based indices and justifies the requirement of these new indices. Further, we propose a method to compute these indices and vertex-degree-based indices from a recently proposed graph matrix, referred to as neighborhood matrix. Computationally, we correlate the proposed indices' efficiency against the octane isomers' and polychlorobiphenyls' physicochemical properties. We perform a comparative study of these indices with a few well-known vertex degree-based indices. Further, the proposed indices' discriminative capacity is analyzed and shown to have higher discriminative power on the considered datasets. Among all the indices under study, four indices, namely AL₄, AL₅, AL₇, and AL₈ have shown the highest discriminative power on the set of octane isomers. While the indices AL₄ and AL₇ have the highest discriminative power on the set of PCB molecules compared to the other VDB indices. Among the proposed and considered indices, we show that the first index AL₁ has a good correlation with the Acentric factor and entropy of octane isomer and with the total surface area, log-water-solubility, relative retention time, octanol-water-partition, and log-water-activity coefficient of PCBs.