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A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree
1PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu 620020 India.
Springerplus
|November 8, 2016
Summary
This study introduces a novel algorithm for identifying fuzzy Hamiltonian cycles in fuzzy graphs. The algorithm utilizes adjacency matrices and vertex degrees for efficient analysis of complex networks like airline routes.
Area of Science:
- Graph Theory
- Computer Science
- Network Analysis
Background:
- Hamiltonian cycles are crucial in graph theory, visiting each vertex once.
- Analyzing large graphs and their Hamiltonian cycles is computationally challenging.
- Fuzzy graph theory offers a framework for handling uncertainty in network structures.
Purpose of the Study:
- To propose a new algorithm for detecting fuzzy Hamiltonian cycles.
- To leverage adjacency matrices and vertex degrees for efficient fuzzy graph analysis.
- To model and illustrate the algorithm's application using a real-world airline network.
Main Methods:
- Representing fuzzy graphs using adjacency matrices.
- Developing an algorithm that incorporates vertex degrees.
- Applying the algorithm to a fuzzy graph model of Indigo airlines' air network.
Main Results:
- The proposed algorithm efficiently finds fuzzy Hamiltonian cycles.
- The adjacency matrix and vertex degree approach simplifies complex graph analysis.
- The Indigo airlines network case study demonstrates practical applicability.
Conclusions:
- The new algorithm provides an effective method for fuzzy Hamiltonian cycle detection.
- Computer-assisted analysis of fuzzy graphs is feasible and beneficial.
- This research contributes to efficient network analysis in fuzzy graph theory.
Keywords:
Adjacency matrixDegree of a vertex in a fuzzy graphFuzzy Hamiltonian cycleFuzzy Hamiltonian pathFuzzy graphMore Related Videos
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