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This study adapts this concept to real-world scenarios, like emergency response systems, by addressing challenges such as roadblocks and traffic congestion. We introduce the secure set and the eternal 1-secure set for fuzzy graphs based on edge membership levels J. Our analysis examines the relationship between the security number of a fuzzy graph G at level J and the domination number of its spanning subgraph at level J, demonstrating the potential of the eternal 1-secure set to enhance security measures in dynamic environments.<\/jats:p>","DOI":"10.3233\/kes-240290","type":"journal-article","created":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T12:49:18Z","timestamp":1721738958000},"page":"647-659","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Eternal 1-security number of a fuzzy graph with level J"],"prefix":"10.1177","volume":"28","author":[{"given":"Mary Jiny","family":"D","sequence":"first","affiliation":[{"name":"Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G.","family":"Navamani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, SIMATS, Chennai, Tamilnadu, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Shanmugapriya","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, Tamil Nadu, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Raman","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Production Engineering, Guru Nanak Dev Engineering College, Ludhiana, Punjab, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"\u017deljko","family":"Stevi\u0107","sequence":"additional","affiliation":[{"name":"University of East Sarajevo, Faculty of Transport and Traffic Engineering, Bosnia and Herzegovina"},{"name":"Department of Industrial and Management Engineering, Korea University, Seoul, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rajender","family":"Kumar","sequence":"additional","affiliation":[{"name":"University Centre for Research and Development, University School of Business, Chandigarh University, Gharuan, Mohali, Punjab, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sandeep","family":"Kumar","sequence":"additional","affiliation":[{"name":"Centre of Research Impact and Outcome, Chitkara University, Rajpura, Punjab, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2024,12,12]]},"reference":[{"issue":"2","key":"bibr1-KES-240290","volume":"2","author":"Xavior DA","year":"2013","journal-title":"International Journal of Computing Algorithm"},{"key":"bibr2-KES-240290","doi-asserted-by":"crossref","unstructured":"Mordeson JN, Mathew S, Malik DS. 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