Dialogue, as a type of semi-structured text, poses significant challenges for generating accurate summaries due to the difficulty in capturing key information dispersed across multiple utterances and understanding the interconnections between them. Existing dialogue summarization methods often fail to fully grasp the deep semantics of dialogues, potentially overlooking important information and resulting in factual inconsistencies. We propose a novel summarization approach that combines dialogue structural features with a post-editing correction mechanism. First, we model the structure of dialogues and introduce a graph encoder. This graph encoder dynamically learns the structural knowledge of dialogues based on the semantic representations encoded by pre-trained language models, and integrates this knowledge into the decoder to enhance summary quality. Additionally, to address the issue of factual inconsistency, we employ a post-editing method to correct errors in the generated summaries. To validate the effectiveness of our approach, we conducted experiments on three datasets. Compared to several strong baselines, our method achieved significant improvements, demonstrating that it not only enhances summary quality but also effectively improves factual consistency.