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Abstract
In this paper, a new concept of fuzzy edge coloring is introduced. The fuzzy edge coloring is an assignment of colors to edges of a fuzzy graph G. It is proper if no two strong adjacent edges of G will receive the same color. Fuzzy edge chromatic number of G is least positive integer for which G has a proper fuzzy edge coloring. In this paper, the fuzzy edge chromatic number of different classes of fuzzy graphs and the fuzzy edge chromatic number of fuzzy line graphs are found. Isochromatic fuzzy graph is also defined.
Highlights
Fuzzy graph theory was introduced by Azriel Rosenfeld in 1975
Fuzzy edge coloring concept can be applied to the problems like job scheduling, register allocation, exam scheduling, time tabling problem, assignment problem etc
Fuzzy chromatic number of a fuzzy graph G is a minimum number of colors needed for proper fuzzy coloring of G
Summary
Fuzzy graph theory was introduced by Azriel Rosenfeld in 1975. Though it is very young, it has numerous applications in almost all fields. Fuzzy graph coloring is one of the most important concepts in fuzzy graph theory. Fuzzy edge coloring concept can be applied to the problems like job scheduling, register allocation, exam scheduling, time tabling problem, assignment problem etc. The fuzzy edge chromatic number of different classes of fuzzy graphs and fuzzy line graphs are discussed. The isochromatic fuzzy graph is defined and some of the isochromatic fuzzy graphs are presented
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