Abstract
Graph is a easy way to represent the real life situation. Graph is a combination of Points and Lines. In network analysis, the degree of a point plays a prominent role in Graph Theory. The degree of a point is the number of connections it has with the other points in the point set. Among the degrees of all the points in graph $G^*$, the minimum value is denoted by $\delta(G^*)$. In this article, a new abstraction of fuzzy graph is initiated by combining the parameters, degree of a point and minimum degree of the graph and termed it is as $\delta_d$-fuzzy graphs. Order and Size on $\delta_d$-fuzzy graphs were studied and Handshaking Lemma were explained with illustration. Idea on $\delta_d$-regular fuzzy graph were interpreted using the theorems. Also operations on graphs such as union, intersection, complement, cartesian product, Tensor Product, Corona are extended for $\delta_d$-fuzzy graphs.
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