A fuzzy soft set is a mapping from parameter set to the fuzzy subsets of universe. Fuzzy soft set theory provides a parameterized point of view for uncertainty modeling and soft computing model. In this research article, we apply the concept of fuzzy soft sets to graphs. We present the concept of fuzzy soft graphs, various methods of their construction, and investigate some of their related properties. We discuss certain types of irregular fuzzy soft graphs. We also describe applications of fuzzy soft graphs in social network and road network.
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