## 4 Materials and Methods  
The main stages of this work are illustrated in Figure 1. The summarization process begins with a preprocessing step applied to the documents. Following this, graphs are generated from the processed texts. In these graphs, relationships between nodes, each representing a sentence, are established based on shared phrases. The next step is the Graph Independent Set analysis, which forms the core of the proposed framework. The MIS is identified on these graphs, and the nodes comprising the independent sets are extracted. This step aims to remove sentence groups represented by the MIS from the graphs. By doing so, repetitive information in the text graphs is eliminated before the quantitative evaluation. This restriction effectively prevents the inclusion of redundant word groups in the summary and addresses the limitations of LLMs. The revised graphs' representative sentences are then passed to the LLMs. This creates a much smaller subset of the original text, enabling LLMs to select sentences more quickly and with better contextual clarity. As a result, LLMs process a considerably more concise dataset compared to the full documents. Sentence coverage scores from XLNet, RoBERTa, DistilBERT, ELECTRA, ALBERT, and Pegasus are used to generate summaries of varying lengths (3, 200, and 400 words). To demonstrate the framework's reliability and robustness, experiments are conducted on two distinct datasets: CNN/DailyMail and DUC-2002. While CNN/DailyMail offers broad, up-to-date news content, DUC-2002 provides more academic and comparative documents. Including both datasets is important to reflect the framework's comprehensiveness, despite structural differences. Significant improvements in summarization quality are observed across both datasets. Additionally, the summarization process becomes notably faster. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Datasets** & **SD** & **MD** & **Data Size** & **Human Annotation** & **Purpose of Use** \\ \hline DUC-2002 & no & yes & 567 document & yes & Information fusion–Content synthesis \\ CNN/DailyMail & yes & no & 290,000 news & yes & Main idea extraction–Summary of information \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of text summarization datasets and their usage purposes. Figure 2 shows the general block diagram of the proposed framework. This framework combines LLMs with graph-based methods for automatic text summarization, enabling LLMs to utilize both conceptual and structural information. The input data consists of texts from the DUC and CNN/DailyMail datasets. To support generalization with quantitative evidence, these texts are preprocessed and simplified while preserving their structural and contextual integrity. In the second stage, a graph representing sentence phrases and terms is generated from the preprocessed data. Analyses based on Graph Independent Set principles are then conducted to identify the most independent nodes. In the third stage, nodes within the MIS cluster representing sentences least related to the main text are removed, resulting in new graphs containing sentences more closely aligned with the main idea. In the fourth stage, the most valuable nodes from these graphs are selected using the eigenvector centrality metric. This step increases the understanding of the framework. Finally, sentences corresponding to nodes with the highest centrality values are identified and selected for further evaluation by LLMs (XLNet, RoBERTa, DistilBERT, ELECTRA, ALBERT, and Pegasus). These pre-trained LLMs perform an additional scoring process on the selected sentences to determine the most suitable candidates for the summary. The refined texts, enriched with structural information, are then input to the LLMs. In the final stage, candidate summaries of the desired lengths are generated from the selected sentences. This framework aims to improve LLMs' summarization efficiency through sentence selection techniques grounded in Graph Independent Set theory.