Eternal 1-security number of a fuzzy graph with level J-Reference-Cited by-同舟云学术

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

Published:2024-07-02 Issue: Volume: Page:1-13
ISSN:1327-2314
Container-title:International Journal of Knowledge-based and Intelligent Engineering Systems
language:
Short-container-title:KES

Author:

D Mary Jiny¹,Navamani G.²,Shanmugapriya R.³,Kumar Raman⁴,Stević Željko⁵⁶,Kumar Rajender⁷,Kumar Sandeep⁸

Affiliation:

1. Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India

2. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, SIMATS, Chennai, Tamilnadu, India

3. Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, Tamil Nadu, India

4. Department of Mechanical and Production Engineering, Guru Nanak Dev Engineering College, Ludhiana, Punjab, India

5. University of East Sarajevo, Faculty of Transport and Traffic Engineering, Bosnia and Herzegovina

6. Department of Industrial and Management Engineering, Korea University, Seoul, Korea

7. University Centre for Research and Development, University School of Business, Chandigarh University, Gharuan, Mohali, Punjab, India

8. Centre of Research Impact and Outcome, Chitkara University, Rajpura, Punjab, India

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.

Publisher

IOS Press

Reference24 articles.

1. On domination in fuzzy graphs;Xavior;International Journal of Computing Algorithm,2013

2. Mordeson JN, Mathew S, Malik DS. Fuzzy graph theory with applications to human trafficking. Berlin: Springer; 2018 Jan 1.

3. Properties of fuzzy labeling graph;Gani;Applied Mathematical Sciences,2012

4. Fuzzy labeling tree;Nagoorgani;International Journal of Pure and Applied Mathematics,2014

5. Fuzzy labeling tree;Nagoorgani;International Journal of Pure and Applied Mathematics,2014