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The development of ultra-dense heterogeneous networks (HetNets) will cause a significant rise in energy consumption with large-scale base station (BS) deployments, requiring cellular networks to be more energy efficient to reduce operational expense and promote sustainability. Cell switching is an effective method to achieve the energy efficiency goals, but traditional heuristic cell switching algorithms are computationally demanding with limited generalization abilities for ultra-dense HetNet applications, motivating the usage of machine learning techniques for adaptive cell switching. Graph neural networks (GNNs) are powerful deep learning models with strong generalization abilities but receive little attention for cell switching. This paper proposes a GNN-based cell switching solution (GBCSS) that has a smaller computational complexity than existing heuristic algorithms. The presented performance evaluation uses the Milan telecommunication dataset based on real-world call detail records, comparing GBCSS with a traditional exhaustive search (ES) algorithm, a state-of-the-art learning-based algorithm, and the baseline without cell switching. Results indicate that GBCSS achieves a 10.41% energy efficiency gain when compared with the baseline and achieves 75.76% of the optimal performance obtained with ES algorithm. The results also demonstrate GBCSS' significant scalability and generalization abilities to differing load conditions and the number of BSs, suggesting this approach is well-suited to ultra-dense HetNet deployment. [ABSTRACT FROM AUTHOR]