### Motivation and Objective  
LLMs have demonstrated a strong performance not only in NLP but also in fields such as image processing and time-series analysis. However, their large size and high computational and training costs limit their deployment on resource-constrained devices. Another important limitation is their reliance on contextual information while overlooking the structural aspects of language. Although existing studies process large-scale content at the conceptual level, they often fail to effectively capture the internal structure of text. As a result, these models struggle to maintain contextual coherence, particularly when summarizing complex documents. This highlights the need for integrating structural information to improve the summarization capabilities of LLMs.  
In this study, a new framework based on the Graph Independent Set is proposed that enables LLMs to be used in inferential text summarization tasks with a high performance and minimum cost. In this study, the MIS algorithm was chosen because it provides a structural filtering mechanism capable of systematically filtering out contextually irrelevant sentences before summarization. While node centrality-based methods are effective in determining the importance of nodes, they fall short in filtering out nodes with a low content contribution. In contrast, MIS prevents redundancy and semantic overlap, resulting in more compact, focused, and diverse summaries. This approach strengthens the semantic integrity by identifying mutually independent nodes, in contrast to centrality-focused methods that may cause repetition by prioritizing highly connected nodes. Our aim within the scope of this study is to eliminate the limitations of LLMs, including their high computational cost, limited scalability, redundancy in outputs, and their inability to utilize structural relationships within text. Collectively, these research questions aim to determine whether integrating MIS-based graph filtering with LLMs can significantly enhance both their summarization accuracy and computational efficiency. Our Graph Independent Set-based study on the effective and efficient use of LLMs seeks answers to the following fundamental research questions;  
* Does the proposed MIS-based framework improve the summarization accuracy compared to existing popular LLMs?
* Can the framework reduce computational costs and increase efficiency in extractive summarization tasks?
* Does integrating structured information into LLMs enable a more precise modeling of cause-effect relationships within texts?
* Can the use of structured information storage mitigate the context loss inherent in transformer architectures?
* Does structured and canonical data storage reduce the energy consumption of LLMs by optimizing data loads, and does this integration strengthen their performance?
* Can the proposed method achieve a high summarization accuracy at a low cost across different LLMs and datasets?  
The remainder of this paper is structured as follows: Section 2 reviews previous studies related to the topic. Section 3 describes the materials and methods used in the study. Section 4 presents the experimental setup and the obtained results. Section 5 discusses the findings. Finally, Section 6 summarizes the paper by highlighting its contributions and offers suggestions for future research.