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We shed light on this structure\u2019s special qualities and potential uses in healthcare by computing several topological indices linked to it through computational research. Furthermore, we use Shannon\u2019s entropy measure to express the information content of the connection-based topological indices in tandem. This method offers a thorough comprehension of the intricate features and structural properties of the triangular \u03b3-graphyne structure. A logarithmic regression model is built to establish a quantifiable relationship between the computed indices and entropy. The SPSS program was used in the development of this model, allowing for a thorough examination of the relationship between structural features and informational entropy. 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