In this paper, motivated by the notion of generalized single-valued neutrosophicgraphs of the first type, we define a new type of neutrosophic graph called the generalized interval- valued neutrosophic graph of first type (GIVNG1) and presented a matrix representation for this graph. Some of the fundamental properties and characteristics of this new concept is also studied. The concept of GIVNG1 is an extension of generalized fuzzy graphs (GFG1) and generalized single-valued neutrosophic graphs of the first type (GSVNG1).
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