The notion of a fuzzy line graph of a fuzzy graph is introduced. We give a necessary and sufficient condition for a fuzzy graph to be isomorphic to its corresponding fuzzy line graph. We examine when an isomorphism between two fuzzy graphs follows from an isomorphism of their corresponding fuzzy line graphs. We give a necessary and sufficient condition for a fuzzy graph to be the fuzzy line graph of some fuzzy graph. © 1993.
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