A review on taxonomy of fuzzy graph

Abstract

Fuzzy graph is a graph that incorporates fuzziness.  Fuzzy graph originated from the concept of Fuzzy Set and Graph.  In this paper, taxonomy of fuzzy graph is reviewed.  Several results on fuzzy graph are presented together with some examples.  The fuzzy graph introduced by Yeh and Bang is proven to be a special case of Rosenfeld’s fuzzy graph.  Two descriptions of isomorphic crisp graph are proven to be equivalent and every crisp isomorphism of two graphs is proven to be a fuzzy isomorphism.  This paper provides an underlying knowledge on fuzzy graph which is an important foundation for further development and application of fuzzy graph.