Intuitionistic fuzzy graph is a highly growing research area dealing with real life applications. In this paper, we introduce the concept of interval valued intuitionistic fuzzy graph and define magic labeling of interval valued intuitionistic fuzzy graph. Here we discuss the significance of magic labeling in interval-valued intuitionistic fuzzy graphs. We also analyse some of its properties and some structures and implement it into the operations of interval-valued intuitionistic fuzzy magic labeling graph. We have also investigated about some bounds over the size and shape of the interval-valued intuitionistic fuzzy graphs based on ε-neighborhood and confine the membership values of the vertices and edges of it.
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