Embedding of fuzzy graphs on topological surfaces

Planar graph is a special type in crisp as well as in fuzzy graphs. In fuzzy planar graphs, the planarity value is the amount of planarity of the crossed fuzzy edges, so that the intersection of fuzzy edges are possible in fuzzy graphs as compared to the planar graphs in crisp. Generally, the fuzzy planar graphs are depicted in the plane surface. In this paper, the embedding of fuzzy graphs are discussed in the surfaces like sphere and m -torus. Moreover, definition of fuzzy planar triangulation, straight-line, and piecewise embedding are also stated for planar embedding. Some of the effective definitions and theorems are illustrated with examples. Theorems like Euler’s formula for plane and sphere surfaces are proved and formulated for fuzzy planar graphs.