Fraud detection is a critical challenge in various domains, such as finance, e-commerce, and cybersecurity, due to the dynamic and complex nature of fraudulent activities. Traditional machine learning approaches often fail to effectively capture the intricate relationships and dependencies present in the underlying data, especially when these relationships can be represented as graphs. This paper presents a novel graph-theoretical approach to fraud detection using Graph Neural Networks (GNNs), leveraging their capability to model non-Euclidean data and learn representations from graph-structured data. By formulating fraud detection as a node classification problem on transaction graphs, we exploit the topological features and connectivity patterns inherent in the data to identify anomalous behaviors. Our proposed framework integrates advanced techniques such as attention mechanisms and message passing to enhance the detection performance. Experiments conducted on benchmark and real-world datasets demonstrate that our model achieves superior accuracy, precision, and recall compared to existing methods. The findings highlight the potential of graph-based methods in detecting sophisticated fraudulent schemes and open new avenues for research in fraud detection using graph-theoretical principles.