Complete Fuzzy Graphs

In this paper, we provide three new operations on fuzzy graphs; namely direct product, semi-strong product and strong product. We give sufficient conditions for each one of them to be complete and we show that if any of these products is complete, then at least one factor is a complete fuzzy graph. Moreover, we introduce and study the notion of balanced fuzzzy graph and give necessary and sufficient conditions for the preceding products of two fuzzy balanced graphs to be balanced and we prove that any isomorphic fuzzy graph to a balanced fuzzy graph must be balanced. Key Words: Neutrosophic set, fuzzy graph, complete fuzzy graph, balanced fuzzy graph. AMS (2010): 05C72.

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