In this paper, we define k-regular chromatic fuzzy graph, 1-factor fuzzy graph and chromatic number of faces. Further, we introduce 3-regular chromatic fuzzy graph theorem, Euler formula and its consequences and provide some related theorems, corollaries, examples discussed.

fuzzy graph, chromatic fuzzy graph, regular fuzzy graph, planar fuzzy graph, 3-regular chromatic fuzzy graph, 1-factor fuzzy graph, antifactor, chromatic number of fuzzy faces, girth of a fuzzy graph.