Abstract
This paper, applies the concept of KM-fuzzy metric spaces and introduces a novel concept of KM-fuzzy metric graphs based on KM-fuzzy metric spaces. This study, investigates the finite KM-fuzzy metric spaces with respect to metrics and KM-fuzzy metrics and constructs KM-fuzzy metric spaces on any given non-empty sets. It tries to extend the concept of KM-fuzzy metric spaces to a larger class of KM-fuzzy metric spaces such as union and product of KM-fuzzy metric spaces and in this regard investigates a class of products of KM-fuzzy metric graphs.
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