We propose a novel methodology for extractive, generic summarization of text documents. The Maximum Independent Set, which has not been used previously in any summarization study, has been utilized within the context of this study. In addition, a text processing tool, which we named KUSH, is suggested in order to preserve the semantic cohesion between sentences in the representation stage of introductory texts. Our anticipation was that the set of sentences corresponding to the nodes in the independent set should be excluded from the summary. Based on this anticipation, the nodes forming the Independent Set on the graphs are identified and removed from the graph. Thus, prior to quantification of the effect of the nodes on the global graph, a limitation is applied on the documents to be summarized. This limitation prevents repetition of word groups to be included in the summary. Performance of the proposed approach on the Document Understanding Conference (DUC-2002 and DUC-2004) datasets was calculated using ROUGE evaluation metrics. The developed model achieved a 0.38072 ROUGE performance value for 100-word summaries, 0.51954 for 200-word summaries, and 0.59208 for 400-word summaries. The values reported throughout the experimental processes of the study reveal the contribution of this innovative method.