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Anti-fuzziness has a vital role in the field of intuitionistic fuzzy theory. In this paper we defined the notion of anti-vertex cover of an intuitionistic anti fuzzy graph. Further we discussed some properties of anti-vertex cover and anti-vertex covering number of intuitionistic anti-fuzzy graphs and derived some theorems too. Anti-Cartesian product of two intuitionistic anti-fuzzy graphs is defined and derived theorems based on that.