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Study on a Strong and Weak n -Connected Total Perfect k -Dominating set in Fuzzy Graphs

Author

Listed:
  • Krishnasamy Elavarasan

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600 062, India)

  • Tharmalingam Gunasekar

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600 062, India)

  • Lenka Cepova

    (Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 708 00 Ostrava, Czech Republic)

  • Robert Cep

    (Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 708 00 Ostrava, Czech Republic)

Abstract

In this paper, the concept of a strong n -Connected Total Perfect k -connected total perfect k -dominating set and a weak n -connected total perfect k -dominating set in fuzzy graphs is introduced. In the current work, the triple-connected total perfect dominating set is modified to an n -connected total perfect k -dominating set n c t p k D (G) and number γ n c t p D ( G ) . New definitions are compared with old ones. Strong and weak n -connected total perfect k -dominating set and number of fuzzy graphs are obtained. The results of those fuzzy sets are discussed with the definitions of spanning fuzzy graphs, strong and weak arcs, dominating sets, perfect dominating sets, generalization of triple-connected total perfect dominating sets of fuzzy graphs, complete, connected, bipartite, cut node, tree, bridge and some other new notions of fuzzy graphs which are analyzed with a strong and weak n c t p k D (G) set of fuzzy graphs. The order and size of the strong and weak n c t p k D ( G ) fuzzy set are studied. Additionally, a few related theorems and statements are analyzed.

Suggested Citation

  • Krishnasamy Elavarasan & Tharmalingam Gunasekar & Lenka Cepova & Robert Cep, 2022. "Study on a Strong and Weak n -Connected Total Perfect k -Dominating set in Fuzzy Graphs," Mathematics, MDPI, vol. 10(17), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3178-:d:905832
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    References listed on IDEAS

    as
    1. Luis Porcuna-Enguix & Elisabeth Bustos-Contell & José Serrano-Madrid & Gregorio Labatut-Serer, 2021. "Constructing the Audit Risk Assessment by the Audit Team Leader When Planning: Using Fuzzy Theory," Mathematics, MDPI, vol. 9(23), pages 1-22, November.
    2. O.T. Manjusha & M.S. Sunitha, 2015. "Strong Domination in Fuzzy Graphs," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 7(3), pages 369-377, September.
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