Traffic prediction is a crucial component of data management systems, leveraging historical data to learn spatio-temporal dynamics for forecasting future traffic and enabling efficient decision-making and resource allocation. Despite efforts to develop increasingly complex architectures, existing traffic prediction models often struggle to generalize across diverse datasets and contexts, limiting their adaptability in real-world applications. In contrast to existing traffic prediction models, large language models (LLMs) progress mainly through parameter expansion and extensive pre-training while maintaining their fundamental structures. In this paper, we propose ST-LLM+, the graph enhanced spatio-temporal large language models for traffic prediction. Through incorporating a proximity-based adjacency matrix derived from the traffic network into the calibrated LLMs, ST-LLM+ captures complex spatio-temporal dependencies within the traffic network. The Partially Frozen Graph Attention (PFGA) module is designed to retain global dependencies learned during LLMs pre-training while modeling localized dependencies specific to the traffic domain. To reduce computational overhead, ST-LLM+ adopts the LoRA-augmented training strategy, allowing attention layers to be fine-tuned with fewer learnable parameters. Comprehensive experiments on real-world traffic datasets demonstrate that ST-LLM+ outperforms state-of-the-art models. In particular, ST-LLM+ also exhibits robust performance in both few-shot and zero-shot prediction scenarios. Additionally, our case study demonstrates that ST-LLM+ captures global and localized dependencies between stations, verifying its effectiveness for traffic prediction tasks.