Eternal 1-security number of a fuzzy graph with level J

Article type: Research Article

Authors: D, Mary Jiny^a | Navamani, G.^b | Shanmugapriya, R.^c | Kumar, Raman^d | Stević, Željko^{e; f; *} | Kumar, Rajender^g | Kumar, Sandeep^h

Affiliations: [a] Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India | [b] Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, SIMATS, Chennai, Tamilnadu, India | [c] Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, Tamil Nadu, India | [d] Department of Mechanical and Production Engineering, Guru Nanak Dev Engineering College, Ludhiana, Punjab, India | [e] University of East Sarajevo, Faculty of Transport and Traffic Engineering, Bosnia and Herzegovina | [f] Department of Industrial and Management Engineering, Korea University, Seoul, Korea | [g] University Centre for Research and Development, University School of Business, Chandigarh University, Gharuan, Mohali, Punjab, India | [h] Centre of Research Impact and Outcome, Chitkara University, Rajpura, Punjab, India

Correspondence: [*] Corresponding author: Željko Stević, University of East Sarajevo, Faculty of Transport and Traffic Engineering, Vojvode Mišića 52, 74000 Doboj, Bosnia and Herzegovina. E-mail: [email protected].

Abstract: The eternal 1-secure set, strategically protects graphical structures against attacks by placing sentinels within dominating sets. 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.

Keywords: Fuzzy graph, fuzzy domination number, eternal 1-security number, fuzzy path, fuzzy cycle

DOI: 10.3233/KES-240290

Journal: International Journal of Knowledge-based and Intelligent Engineering Systems, vol. Pre-press, no. Pre-press, pp. 1-13, 2024