Large Language Models (LLMs) have significantly advanced the capabilities of dialogue systems, yet they often lack controllability and consistency. My research investigates how explicit structure can be used to guide LLM-based dialogue systems, focusing in particular on graph-based methods. One line of work explores the use of dialogue flow graphs to represent possible user and system actions, enabling systems to constrain generation to goal-directed paths. These graphs serve as an interpretable interface between high-level dialogue policy and low-level natural language output, improving reliability and transparency. In parallel, I examine Retrieval-Augmented Generation (RAG) approaches that leverage knowledge graphs to ground responses in structured background information. I have evaluated how GraphRAG performs on dialogue data and contributed to methods for retrieving compact, relevant subgraphs to support contextually appropriate and verifiable responses. These approaches address the limitations of unguided retrieval and help integrate external knowledge into the generation process more effectively. Together, these directions aim to improve the controllability, grounding, and robustness of LLM-based dialogue systems. I am particularly interested in how graph-based representations can be used not only to structure knowledge, but also to inform and constrain interaction patterns.