This study examines the correlation of connection number-based topological indices with the Gibbs energy of semiconducting carbon allotropes using chemical graph theory. Various indices including Zagreb connection indices, modified Zagreb connection indices, and other molecular descriptors are computed and compared. Curve fitting using MATLAB is carried out to identify precise mathematical correlation between these indices and Gibbs energy. The results indicate important correlations, confirming the validity of the proposed indices in predicting thermodynamic behavior. The study broadens the field of understanding of molecular descriptors in energy research and provides a platform for future computational modeling in the area of material science and nanotechnology. [ABSTRACT FROM AUTHOR]

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