Spectral analysis of Cupric oxide (CuO) and Graphene Oxide (GO) via machine learning techniques

초록

Chemical graph theory has recently gained much attraction among researchers due to its extensive use in mathematical chemistry. In this research article, We have studied the spectral properties such as eigenvalues, energy and Estrada index of some chemical structures such as Cupric oxide (CuO) and Graphene Oxide (GO). We have computed the energy E(G)=∑i=0n|λi| and the other invariant Estrada index EE(G)=∑i=1neλ of the above mentioned graph structures and obtain the polynomial regression analysis using machine learning techniques. This approach permitted us to predict the spectral values more precisely and analyze the difference between the actual and predicted values. The actual values of energy and Estrada index is represented by Eav and EEav while the predicted values of energy and Estrada index is represented by Epv and EEpv, where av represents ”actual value” and pv represents ”predicted value”. We first use traditional method based on softwares and get the actual values (av) (see section 2). Then we perform machine learning techniques to generate a best fit model and get the predicted values (pv) of the energies and Estrada index of Cupric oxide CuO and Graphene Oxide GO by using the best fit second order polynomial for Energy and Estrada Index of CuO is obtained as E(CuO)=−0.007m2+5.892mn+2.243m+2.169n−0.365 and EE(CuO)=0.537+2.084m+2.084n+13.533mn, respectively. Similarly, the best fit second order polynomial for Energy and Estrada Index of GO is obtained as E(GO)=−0.266+2.533m+2.598n+0.014m2+3.133mn+−0.017n2 and EE(GO)=−1.671+4.400m+4.440n+0.016m2+6.553mn+0.014n2, respectively. We have observed the difference between av and pv which shows our machine learning model is best fit model as the error between the av and pv is minimum. © 2025 The Authors

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