Theoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. The concept of interval-valued intuitionistic fuzzy set was introduced by Atanassov [3]. Interval-valued intuitionistic fuzzy sets provide a more adequate description of uncertainly 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 the authors introduced the concepts of m-polar interval-valued intuitionistic fuzzy graph (IVIFG), edge regular m-polar IVIFG, totally edge regular m-polar IVIFG and highly irregular m-polar IVIFG.
