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Applications of maximum matching by using bipolar fuzzy incidence graphs
Fahad Ur Rehman1, Tabasam Rashid1, Muhammad Tanveer Hussain1
1Department of Mathematics, University of Management and Technology (UMT), Lahore, Pakistan.
This study introduces matching concepts in bipolar fuzzy incidence graphs (BFIGs), extending fuzzy graph theories. Findings offer practical applications in personnel selection and conflict resolution within companies.
Area of Science:
- Graph Theory
- Fuzzy Mathematics
- Discrete Mathematics
Background:
- Bipolar fuzzy graphs are extended to bipolar fuzzy incidence graphs (BFIGs) to analyze vertex-edge effects.
- Existing fuzzy graph theorems require adaptation for BFIGs.
Purpose of the Study:
- Introduce and investigate matching concepts within bipartite BFIGs and general BFIGs.
- Extend existing fuzzy graph results to the domain of BFIGs.
- Analyze operations like augmenting paths and principal numbers in BFIGs.
Main Methods:
- Definition of matching in bipartite BFIGs and BFIGs.
- Investigation of augmenting paths and matching principal numbers.
- Extension of fuzzy graph theorems to BFIGs.
Main Results:
- Established theorems and results for matching in BFIGs.
- Characterized maximum matching principal numbers in BFIGs.
- Demonstrated the applicability of matching concepts in BFIGs.
Conclusions:
- Matching concepts are effectively applied to BFIGs and bipartite BFIGs.
- The study provides tools for vertex and incidence pair fuzzy maximization problems.
- Results are beneficial for practical applications like employee selection and minimizing company losses.
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