In this work, a quantitative structure property relationship analysis is performed for selected \(\beta\) -lactam antibiotics using eigenvalue based spectral descriptors derived from molecular graph representations. Molecular structures are modeled as graphs, and spectral indices obtained from adjacency, Laplacian, signless Laplacian, and distance matrices are employed to encode global topological characteristics. Non linear regression models, including quadratic, logarithmic, and power forms, are used to investigate relationships between spectral descriptors and physicochemical properties such as boiling point, molar volume, molar refractivity, polar surface area, and surface tension. The results indicate that several spectral descriptors exhibit meaningful correlations with properties primarily governed by molecular size and connectivity. Among the considered models, quadratic regression generally shows marginally improved performance, reflected by higher coefficients of determination and lower prediction errors. In contrast, properties strongly influenced by electronic and surface specific effects display weaker correlations, highlighting the intrinsic limitations of purely graph based descriptors. Overall, the findings demonstrate the applicability of spectral graph descriptors as interpretable tools for QSPR modeling of \(\beta\) -lactam antibiotics and provide a basis for further studies involving larger datasets and complementary descriptor classes.
