M. Hamidi - Department of Mathematics, Faculty of Mathematics, Payame Noor University, Tehran, Iran
S. Jahanpanah - Department of Mathematics, Faculty of Mathematics, Payame Noor University, Tehran, Iran
A. Radfar - Department of Mathematics, Faculty of Mathematics, Payame Noor University, Tehran, Iran

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.

KM-Fuzzy metric space, t-norm, (derivable) KM-fuzzy metric graph, C-graphable