<p>Topological indices play a crucial role in the prediction of physicochemical and biological properties of molecules. Recently, Ivan Gutman introduced the Sombor index, a new vertex-degree-based topological index that possesses significant geometric meaning. Since its introduction, this index has garnered substantial attention in mathematical chemistry and graph theory, leading to a surge in research exploring its properties, applications, and extensions. Motivated by its geometric foundation, we investigate in this paper various generalizations of the integral Sombor indices, analyzing their structural characteristics and mathematical implications. In addition, we study the applications of these indices in modeling the entropy of octane isomers.</p>