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In this paper, the concept of minimal intuitionistic dominating vertex subset of an intuitionistic fuzzy graph was considered, and on its basis, the notion of a domination set as an invariant of the intuitionistic fuzzy graph was introduced. A method and an algorithm for finding all minimal intuitionistic dominating vertex subset and domination set was proposed. This method is the generalization of Maghout's method for fuzzy graphs. The example of finding the domination set of the intuitionistic fuzzy graph were considered as well.

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