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

Manimozhi Vasuki, Ramachandramoorthi Shanmugapriya, Miroslav Mahdal and Robert Cep ()
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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

Mathematics, 2023, vol. 11, issue 2, 1-9

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.

Keywords: fuzzy graph; fuzzy resolving set; resolving dominating set; fuzzy resolving number; fuzzy resolving domination (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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