In this paper, lexicographic products of two intuitionistic fuzzy graphs, namely, lexicographic min product and lexicographic max product which are analogous to the concept lexicographic product in crisp graph theory are defined. It is illustrated that the operations lexicographic products are not commutative. The connected effective and complete properties of the operations lexicographic products are studied. The degree of a vertex in the lexicographic products of two intuitionistic fuzzy graph is obtained. A relationship between the lexicographic min product and lexicographic max–product is also obtained.
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