Abstract

Topological descriptors play an important role in chemical graph theory and QSPR/QSAR studies by relating molecular structure to measurable physicochemical properties. Among standard benchmark families, octane isomers are frequently used to evaluate the behavior of degree-based descriptors because of their rich branching patterns and well-documented physicochemical data. Although many studies have examined topological indices for octane isomers, comparatively fewer works have focused on topological coindices and derived coindex-based descriptors. In this work, we study several known topological coindices and four derived descriptors, denoted by KJ1,KJ2,KJ3, and KJ4, for comparative analysis on the octane-isomer benchmark. We also present a unified treatment of lower and upper bounds for the first and second (α,β)-general Zagreb indices, together with their reduced and expanded variants, in terms of basic graph parameters, such as the minimum degree, maximum degree, order, and size. These bounds cover a range of familiar special cases, including classical Zagreb, forgotten, Sombor, and Randić-type indices, thereby placing several known descriptors within a common framework. For the application part, the original octane-isomer analysis is retained as a controlled benchmark for the proposed descriptors. In addition, an expanded QSPR experiment is added using a Zenodo molecular dataset containing 90 organic compounds and nine physicochemical endpoints. SMILES strings were converted into hydrogen-suppressed molecular graphs, graph-theoretical descriptors were computed, and ordinary least squares, ridge regression, and PLS(2) models were evaluated using an 80:20 train/test split and five-fold cross-validation. The expanded results show strong or useful performance for selected endpoints, especially critical volume, molecular volume, standard Gibbs free energy of formation, and logarithmic water solubility, whereas some temperature-related endpoints remain less stable. The results therefore support the usefulness of degree-based and coindex-based descriptors as compact exploratory QSPR variables while also emphasizing the need for cautious interpretation, redundancy analysis, and external validation on broader chemical families.

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