Handling graph data is one of the most difficult tasks. Traditional techniques, such as those based on geometry and matrix factorization, rely on assumptions about the data relations that become inadequate when handling large and complex graph data. On the other hand, deep learning approaches demonstrate promising results in handling large graph data, but they often fall short of providing interpretable explanations. To equip the graph processing with both high accuracy and explainability, we introduce a novel approach that harnesses the power of a large language model (LLM), enhanced by an uncertainty-aware module to provide a confidence score on the generated answer. We experiment with our approach on two graph processing tasks: few-shot knowledge graph completion and graph classification. Our results demonstrate that through parameter efficient fine-tuning, the LLM surpasses state-of-the-art algorithms by a substantial margin across ten diverse benchmark datasets. Moreover, to address the challenge of explainability, we propose an uncertainty estimation based on perturbation, along with a calibration scheme to quantify the confidence scores of the generated answers. Our confidence measure achieves an AUC of 0.8 or higher on seven out of the ten datasets in predicting the correctness of the answer generated by LLM.