The adoption of Large Language Models (LLMs) is rapidly expanding across various tasks that involve inherent graphical structures. Graphs are integral to a wide range of applications, including motion planning for autonomous vehicles, social networks, scene understanding, and knowledge graphs. Many problems, even those not initially perceived as graph-based, can be effectively addressed through graph theory. However, when applied to these tasks, LLMs often encounter challenges, such as hallucinations and mathematical inaccuracies. To overcome these limitations, we propose Graph-Grounded LLMs, a system that improves LLM performance on graph-related tasks by integrating a graph library through function calls. By grounding LLMs in this manner, we demonstrate significant reductions in hallucinations and improved mathematical accuracy in solving graph-based problems, as evidenced by the performance on the NLGraph benchmark. Finally, we showcase a disaster rescue application where the Graph-Grounded LLM acts as a decision-support system.