## 3 Methodology
### Graph-CoT Prompt Construction  
CoT prompting is a method to boost the reasoning ability of LLMs by explicitly breaking down the reasoning process, allowing the model to derive answers step by step. Graph-CoT extends the CoT idea to KGs, enabling LLMs to perform stepwise reasoning with the help of the KG's entity-relation structure. In this work, we incorporate Graph-CoT into LLM reasoning for KGC by designing a prompt template that infuses multi-hop KG reasoning into LLMs' thought process. Our Graph-CoT prompt construction is as follows.  
The entire prompt consists of three parts, namely the input, the intermediate reasoning process, and the output. The input section explicitly defines the task background and constrains the model to perform reasoning within a predefined set of candidate tail entities, thereby avoiding unreasonable answers that may arise from open-ended generation. Given a descriptive sentence such as _\"The director of Avatar is [PERSON]\"_, we can extract the corresponding head entity and relation to construct the query triple to be predicted. Then, combined with the candidate entity set, the task instruction prompt model is constructed to select the most appropriate tail entity in the limited set. The prompt is designed following the structure illustrated in Figure 3.  
The intermediate reasoning process provides structured knowledge to facilitate reasoning, which contains two types of supporting information. The first category includes known triples that either have an identical head entity or are linked by an identical relation  
Figure 3: An example of a Graph-CoT prompt. The natural language task instruction serves as the input, which is combined with structured contextual information to guide LLMs in performing chain-of-thought reasoning within a restricted candidate space and generating an answer accompanied by an explanation.  
Figure 2: Overall architecture of the GLR framework. The diagram shows the complete workflow of GLR, including the three core modules: Graph-CoT prompt generation, LoRA fine-tuning, and P(True) confidence evaluation. These components work together to guide structured reasoning, adapt the model to the KG domain, and assess prediction confidence.  
to the query triple, thereby offering structural context and indicative relational patterns. For example, triples such as (\"_Avatar_\", \"_producer_\", \"_[PERSON]_\") and (\"_Titanic_\", \"_director_\", \"_[PERSON]_\") help verify the rationality of candidate tail entities. The second type of supporting information consists of known triples where the head entity of the query appears as the tail entity, offering contextual information about the head entity Avatar in the KG. For instance, (\"_20 th Century Fox_\", \"_produced_\", \"_Avatar_\") provides contextual clues to help the model better understand the semantic role of the head entity. With the assistance of these two types of structural information, LLMs can perform more effective structured reasoning, thereby improving the accuracy of their predictions.  
In the output section, the model selects the most appropriate tail entity based on the provided structured information and generates an explanation, ensuring the interpretability and rationality of the prediction results. An example of such a prompt construction is illustrated in Figure 3.  
Through the design of the Graph-CoT prompt, the model can fully leverage multi-hop contextual information, explicitly presenting the originally implicit reasoning chains in the graph structure within the prompt of LLMs, thereby enhancing the accuracy of the final reasoning results.