Sharp upper bounds for Sombor indices of acyclic graphs with chemical applicability

Abstract Graph-based molecular descriptors are fundamental tools in mathematical chemistry, providing critical insights into molecular properties such as stability, branching, and reactivity. In this work, we conduct a comprehensive investigation of extremal values for several Sombor indices ( SO , $$SO_3$$ S O 3 , $$SO_4$$ S O 4 , $$SO_6$$ S O 6 ) within a specific class of tree structures with a given order and number of segments. To demonstrate practical relevance, we apply these theoretical results to the analysis of 18 octane isomers, employing statistical methods to assess correlations with seven key physicochemical properties. The study reveals strong predictive power for entropy ( $$R^2>0.88$$ R 2 > 0.88 ) and significant correlations with boiling point and density, while also highlighting limitations in lipophilicity estimation.