In this research article, we present a novel frame work for handling intuitionistic fuzzy soft information by combining the theory of intuitionistic fuzzy soft sets with graphs. We present the concepts of intuitionistic fuzzy soft graphs, regular intuitionistic fuzzy soft graphs and irregular intuitionistic fuzzy soft graphs. We illustrate these concepts by describing several examples. We investigate some of their related properties. We introduce the notion of edge regular intuitionistic fuzzy soft graphs and present some of their interesting properties. We also present an application of intuitionistic fuzzy soft graphs in decision-making.
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