The concepts of fuzzy labeling and fuzzy magic labeling graph are introduced.Fuzzy magic labeling for some graphs like path, cycle, and star graph is defined.It is proved that every fuzzy magic graph is starburst halloween mix a fuzzy labeling graph, but the converse is not true.We have ninkasi lager shown that the removal of a fuzzy bridge from a fuzzy magic cycle with odd nodes reduces the strength of a fuzzy magic cycle.Some properties related to fuzzy bridge and fuzzy cut node have also been discussed.