The concept of interval-valued intuitionistic fuzzy set was introduced by Atanassov (See [6]). Interval-valued intuitionistic fuzzy sets provide a more adequate description of uncertainty than the traditional fuzzy sets. It has many applications in fuzzy control and the most computationally intensive part of fuzzy control is defuzzification. In this paper, firstly different kinds of interval valued intuitionistic (S, T)-fuzzy graphs are defined. We introduced several types of arcs in the interval valued intuitionistic (S, T)-fuzzy graphs and studied their properties. These arcs are used to study the structure of complete interval valued intuitionistic (S, T)-fuzzy graphs and constant interval valued intuitionistic (S, T)-fuzzy graphs.
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