Graph recommendation methods, representing a connected interaction perspective, reformulate user-item interactions as graphs to leverage graph structure and topology to recommend and have proved practical effectiveness at scale. Large language models, representing a textual generative perspective, excel at modeling user languages, understanding behavioral contexts, capturing user-item semantic relationships, analyzing textual sentiments, and generating coherent and contextually relevant texts as recommendations. However, there is a gap between the connected graph perspective and the text generation perspective as the task formulations are different. A research question arises: how can we effectively integrate the two perspectives for more personalized recsys? To fill this gap, we propose to incorporate graph-edge information into LLMs via prompt and attention innovations. We reformulate recommendations as a probabilistic generative problem using prompts. We develop a framework to incorporate graph edge information from the prompt and attention mechanisms for graph-structured LLM recommendations. We develop a new prompt design that brings in both first-order and second-order graph relationships; we devise an improved LLM attention mechanism to embed direct the spatial and connectivity information of edges. Our evaluation of real-world datasets demonstrates the framework's ability to understand connectivity information in graph data and to improve the relevance and quality of recommendation results.