Options trading volume has grown rapidly in recent years, particularly for index options on the S&P 500. With this surge, market stability and accurate volatility estimation have become more important than ever. Accurate construction of the implied volatility surface (IVS) is essential for derivative pricing and financial risk management. While traditional parametric models such as SVI and SSVI offer arbitrage-free structures, they require frequent recalibration and often perform poorly in the presence of sparse option data. Recent advances in neural operator learning, particularly Graph Neural Operators (GNO), provide a promising data-driven alternative by enabling flexible interpolation without restrictive structural assumptions. However, GNOs involve high-dimensional intermediate representations, incur substantial computational costs, and require large volumes of high-frequency training data, which are often difficult to obtain in practice. This research proposes enhancing the GNO framework by integrating B-spline interpolation into the input representation, significantly improving computational efficiency. By enhancing structural information prior to learning, the method is expected to improve robustness and accuracy in constructing smooth, arbitrage-consistent volatility surfaces. The proposed framework will be evaluated using index option data, contributing to the development of more data-efficient, operator-based approaches in financial modeling.