A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree.
A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. As the number of vertices and edges grow, it becomes very difficult to keep track of all the different ways through which the vertices are connected. Hence, analysis of large graphs can be efficiently done with the assistance of a computer system that interprets graphs as matrices. And, of course, a good and well written algorithm will expedite the analysis even faster. The most convenient way to quickly test whether there is an edge between two vertices is to represent graphs using adjacent matrices. In this paper, a new algorithm is proposed to find fuzzy Hamiltonian cycle using adjacency matrix and the degree of the vertices of a fuzzy graph. A fuzzy graph structure is also modeled to illustrate the proposed algorithms with the selected air network of Indigo airlines.
PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu 620020 India.
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Nagoor Gani
Department of Mathematics, Sona College of Technology (Autonomous), Salem, Tamil Nadu 636 005 India.
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Latha
Adjacency matrix; Degree of a vertex in a fuzzy graph; Fuzzy Hamiltonian cycle; Fuzzy Hamiltonian path; Fuzzy graph