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Interval Valued Intuitionistic Fuzzy Line Graphs.

V N Srinivasa Rao Repalle1, Keneni Abera Tola2, Mamo Abebe Ashebo2

  • 1Department of Mathematics, Wollega University, Nekemte, Ethiopia. rvnrepalle@gmail.com.

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Summary
This summary is machine-generated.

This study introduces interval-valued intuitionistic fuzzy line graphs (IVIFLG) to address uncertainty in graph theory. Key propositions and isomorphism properties of IVIFLGs were established and verified.

Keywords:
Fuzzy setInterval-valued intuitionistic fuzzy graphInterval-valued intuitionistic fuzzy line graphIsomorphism

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Area of Science:

  • Graph Theory
  • Fuzzy Set Theory
  • Uncertainty Quantification

Background:

  • Intuitionistic fuzzy sets are valuable for modeling imprecise and uncertain data.
  • Graph theory provides frameworks for complex relationships.
  • Handling uncertainty in graph structures is an ongoing challenge.

Purpose of the Study:

  • To introduce and define interval-valued intuitionistic fuzzy line graphs (IVIFLG).
  • To explore fundamental properties and theorems of IVIFLG.
  • To investigate isomorphism between IVIFLGs and their underlying intuitionistic fuzzy graphs (IVIG).

Main Methods:

  • Definition of IVIFLG based on intuitionistic fuzzy graphs (IVIG).
  • Development and proof of theoretical propositions concerning IVIFLG properties.
  • Analysis of isomorphism conditions between IVIFLG and IVIG.

Main Results:

  • Several propositions and theorems regarding IVIFLG were formally proposed and proven.
  • The isomorphism between two IVIFLGs and their corresponding IVIGs was determined.
  • The established theorems provide a foundational understanding of IVIFLG structures.

Conclusions:

  • IVIFLG offers a robust framework for analyzing uncertain graph data.
  • The study successfully established key theoretical properties and isomorphism criteria for IVIFLG.
  • This work contributes to the advancement of fuzzy graph theory in handling complex, uncertain systems.