Graph Neural Networks (GNNs) have become a core tool for graph representation learning, and GNNs perform well in tasks such as graph classification, node classification, link prediction, etc. This is due to the efficient capture of graph topology and feature information through a message-passing mechanism. However, traditional GNNs have limitations in effectively identifying structural differences, such as different rings, strongly regular graphs, and graphs with the same local patterns but different global topologies. Considering the importance of articulation points and bridges in the graph structure, especially applied to complex graph structures such as modular and decomposed structures in graphs, identification and robustness of key nodes in networks, subtle connectivity differences in strongly regular graphs. By focusing on these complex graph structures, GNNs can understand the topological properties of graphs more accurately. Hence, this paper proposes a novel graph neural network model, AB-AgentNet, which enhances the structured encoding of graphs by specially encoding the feature information of articulation points and bridges in the graph. This information enhancement helps the GNN to better capture the global structural features that may be ignored by traditional GNN methods when dealing with complex graph structures, which in turn improves the expressive power and application range of the model. Extensive comparative experiments have been conducted on real-world benchmark datasets for graph classification tasks, and the results demonstrate a significant improvement in the accuracy of AB-AgentNet.