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A Study on Fuzzy Resolving Domination Sets and Their Application in Network Theory

Author

Listed:
  • Manimozhi Vasuki

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

  • Ramachandramoorthi Shanmugapriya

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

  • Miroslav Mahdal

    (Department of Control Systems and Instrumentation, 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

Consider a simple connected fuzzy graph (FG) G and consider an ordered fuzzy subset H = {( u 1 , σ ( u 1 )), ( u 2 , σ ( u 2 )), …( u k , σ ( u k ))}, | H | ≥ 2 of a fuzzy graph; then, the representation of σ − H is an ordered k-tuple with regard to H of G. If any two elements of σ − H do not have any distinct representation with regard to H , then this subset is called a fuzzy resolving set (FRS) and the smallest cardinality of this set is known as a fuzzy resolving number (FRN) and it is denoted by Fr(G) . Similarly, consider a subset S such that for any u ∈ S , ∃ v ∈ V − S , then S is called a fuzzy dominating set only if u is a strong arc. Now, again consider a subset F which is both a resolving and dominating set, then it is called a fuzzy resolving domination set (FRDS) and the smallest cardinality of this set is known as the fuzzy resolving domination number (FRDN) and it is denoted by F γr (G) . We have defined a few basic properties and theorems based on this FRDN and also developed an application for social network connection. Moreover, a few related statements and illustrations are discussed in order to strengthen the concept.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:317-:d:1028189
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    References listed on IDEAS

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    1. Shanookha Ali & Sunil Mathew & John N. Mordeson & Hossein Rashmanlou, 2018. "Vertex Connectivity of Fuzzy Graphs with Applications to Human Trafficking," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 457-485, November.
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    Cited by:

    1. 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.

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