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A Study of Independency on Fuzzy Resolving Sets of Labelling Graphs

Author

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  • Ramachandramoorthi Shanmugapriya

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India)

  • Perichetla Kandaswamy Hemalatha

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India)

  • Lenka Cepova

    (Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic)

  • Jiri Struz

    (Department of Machine Parts and Mechanism, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic)

Abstract

Considering a fuzzy graph G is simple and can be connected and considered as a subset H = u 1 , σ u 1 , u 2 , σ u 2 , … u k , σ u k , | H | ≥ 2 ; then, every two pairs of elements of σ − H have a unique depiction with the relation of H , and H can be termed as a fuzzy resolving set (FRS). The minimal H cardinality is regarded as the fuzzy resolving number (FRN), and it is signified by F r G . An independence set is discussed on the FRS, fuzzy resolving domination set (FRDS), and Fuzzy modified antimagic resolving set (FMARS). In this paper, we discuss the independency of FRS and FMARS in which an application has also been developed.

Suggested Citation

  • Ramachandramoorthi Shanmugapriya & Perichetla Kandaswamy Hemalatha & Lenka Cepova & Jiri Struz, 2023. "A Study of Independency on Fuzzy Resolving Sets of Labelling Graphs," Mathematics, MDPI, vol. 11(16), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3440-:d:1212729
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    References listed on IDEAS

    as
    1. Manimozhi Vasuki & Ramachandramoorthi Shanmugapriya & Miroslav Mahdal & Robert Cep, 2023. "A Study on Fuzzy Resolving Domination Sets and Their Application in Network Theory," Mathematics, MDPI, vol. 11(2), pages 1-9, January.
    2. Xiaoliang Xie & Linglu Huang & Stephen M. Marson & Guo Wei, 2023. "Emergency response process for sudden rainstorm and flooding: scenario deduction and Bayesian network analysis using evidence theory and knowledge meta-theory," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 117(3), pages 3307-3329, July.
    3. Xiaoliang Xie & Bingqi Xie & Jiaqi Cheng & Qi Chu & Thomas Dooling, 2021. "A simple Monte Carlo method for estimating the chance of a cyclone impact," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 107(3), pages 2573-2582, July.
    4. Batyr Orazbayev & Ainur Zhumadillayeva & Kulman Orazbayeva & Sandugash Iskakova & Balbupe Utenova & Farit Gazizov & Svetlana Ilyashenko & Olga Afanaseva, 2022. "The System of Models and Optimization of Operating Modes of a Catalytic Reforming Unit Using Initial Fuzzy Information," Energies, MDPI, vol. 15(4), pages 1-25, February.
    5. Xuan Liu & Tianyi Shi & Guohui Zhou & Mingzhe Liu & Zhengtong Yin & Lirong Yin & Wenfeng Zheng, 2023. "Emotion classification for short texts: an improved multi-label method," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-9, December.
    6. A. Nagoor Gani & Muhammad Akram & D. Rajalaxmi (a) Subahashini, 2014. "Novel Properties of Fuzzy Labeling Graphs," Journal of Mathematics, Hindawi, vol. 2014, pages 1-6, July.
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