Large language models (LLMs) have shown strong performance in zero-shot summarization, but often struggle to model document structure and identify salient information in long texts. In this work, we introduce StrucSum, a training-free prompting framework that enhances LLM reasoning through sentence-level graph structures. StrucSum injects structural signals into prompts via three targeted strategies: Neighbor-Aware Prompting (NAP) for local context, Centrality-Aware Prompting (CAP) for importance estimation, and Centrality-Guided Masking (CGM) for efficient input reduction. Experiments on ArXiv, PubMed, and Multi-News demonstrate that StrucSum consistently improves both summary quality and factual consistency over unsupervised baselines and vanilla prompting. In particular, on ArXiv, it increases FactCC and SummaC by 19.2\% and 8.0\% points, demonstrating stronger alignment between summaries and source content. The ablation study shows that the combination of multiple strategies does not yield clear performance gains; therefore, structure-aware prompting with graph-based information represents a promising and underexplored direction for the advancement of zero-shot extractive summarization with LLMs. Our source code is publicly available.

翻译：大语言模型（LLM）在零样本摘要任务中展现出强大性能，但在长文本中往往难以建模文档结构并识别关键信息。本文提出StrucSum，一种无需训练的提示框架，通过句子级图结构增强LLM的推理能力。StrucSum通过三种针对性策略将结构信号注入提示：面向局部上下文的邻域感知提示（NAP）、面向重要性估计的中心性感知提示（CAP），以及面向高效输入缩减的中心性引导掩码（CGM）。在ArXiv、PubMed和Multi-News数据集上的实验表明，相较于无监督基线和原始提示方法，StrucSum能持续提升摘要质量与事实一致性。尤其在ArXiv数据集上，其FactCC与SummaC指标分别提升19.2%和8.0个百分点，证明摘要与源内容具有更强的对齐性。消融研究表明，多种策略的组合并未带来明显的性能增益；因此，基于图信息的结构感知提示为推进LLM零样本抽取式摘要的发展提供了一个具有潜力且尚未充分探索的研究方向。本研究源代码已公开。