<![CDATA[Xanthone is a heterocyclic compound with various substituents (hydroxy, prenyl, geranyl, methoxy, halogens, and others). The presence of these substituents contributes to diverse biological activities, including anticancer, antidiabetic, and antioxidant properties. This study aims to optimize the design of xanthone derivatives through a mathematical approach using Chemical Topological Graphs (CTG) and the Atom-Bond Connectivity (ABC) index. A literature review was conducted to identify the physicochemical properties, biological activities, and molecular structures of compounds such as 1,7-dihydroxy-3-methoxy-2-(3-methylbut-2-enyl)xanthone (1), Gartanin (2), and Garcinon (3). These xanthone derivatives are distinguished by the number of prenyl substitutions on their core structures. Chemical graph theory is employed to represent molecular structures, with atoms represented as nodes and chemical bonds as edges. The ABC index is calculated based on the degree of connected atoms within the molecules and correlated with the compounds’ physicochemical properties and bioactivity. The ABC index values for compounds (1), (2), and (3) are 32.186, 43.987, and 51.744, respectively. These values indicate that an increase in prenyl substitutions leads to higher ABC index values, which correspond to decreased polarity, increased boiling points, and enhanced bioactivity and stability of the xanthone derivatives]]>
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