The stability of a network is measured by vulnerability parameters. Integrity is one the most important vulnerability parameter in the field of graph network. An uncertain network can be modeled as a fuzzy graph. In this paper, vertex integrity of fuzzy graph is introduced and illustrated with example. Also, we introduced the vertex integrity of the union, join and Cartesian product of two fuzzy graphs and established many interesting results on them. Finally, we discussed edge integrity of fuzzy graph with suitable illustration and investigated many results on edge integrity of fuzzy graph.
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