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Completeness and regularity of generalized fuzzy graphs.
Sovan Samanta1, Biswajit Sarkar1, Dongmin Shin1
1Department of Industrial and Management Engineering, Hanyang University, Ansan, Gyeonggi 15588 South Korea.
Springerplus
|December 6, 2016
Summary
Generalized fuzzy graphs overcome limitations of standard fuzzy graphs for complex systems. This study introduces generalized fuzzy graphs, their matrix representation, and properties of regular and complete generalized fuzzy graphs.
Area of Science:
- Graph Theory
- Discrete Mathematics
- Computer Science
Background:
- Fuzzy graphs are essential for modeling real-world systems like networks and scheduling.
- Standard fuzzy graphs have limitations due to edge restrictions, hindering their application in certain domains.
- Generalized fuzzy graphs offer a more flexible framework to overcome these limitations.
Purpose of the Study:
- Introduce the concept and formal definition of generalized fuzzy graphs.
- Describe the matrix representation for generalized fuzzy graphs.
- Define and investigate properties of regular and complete generalized fuzzy graphs.
Main Methods:
- Development of theoretical framework for generalized fuzzy graphs.
- Formulation of matrix representations for these graphs.
- Analysis of graph properties including regularity and completeness.
Main Results:
- Introduction of generalized fuzzy graphs as an extension of traditional fuzzy graphs.
- Description of matrix representation techniques applicable to generalized fuzzy graphs.
- Characterization of regular and complete generalized fuzzy graphs with discussion of their properties.
Conclusions:
- Generalized fuzzy graphs provide a more robust model for complex systems compared to standard fuzzy graphs.
- Matrix representations offer a systematic way to analyze generalized fuzzy graphs.
- The study lays the groundwork for further research into the applications of regular and complete generalized fuzzy graphs.
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