Intuitionistic fuzzy graph is a highly growing research area dealing with real life applications. In this paper, we introduced the concept of interval valued intuitionistic fuzzy graphs and defined Bi-Magic labeling of interval valued intuitionistic fuzzy graphs. Here, we discussed the significance of Bi-Magic labeling in interval-valued intuitionistic fuzzy graphs. We also analyzed some of the properties and structures and implemented them in the operations of interval-valued intuitionistic fuzzy Bi-Magic labeling graphs. We have also investigated the existence of some bounds over the size and shape of the interval-valued intuitionistic fuzzy graphs based on δ-neighborhood and confined the membership values of the vertices and edges of them.
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