Concept of fuzzy planar graphs

Fuzzy graph is now a very important research area due to its wide application. Fuzzy multigraph and fuzzy planar graphs are two subclasses of fuzzy graph theory. In this paper, we define both of these graphs and studied a lot of properties. A very close association of fuzzy planar graph is fuzzy dual graph. This is also defined and studied several properties. The relation between fuzzy planar graph and fuzzy dual graph is also established.