Let  be a fuzzy graph. There are results for a crisp graph which does not hold generally for a fuzzy graph. In this paper, we constructed a fuzzy graph Gas a counterexample of some results on domination of a fuzzy graph in [9], split domination of a fuzzy graph in [3], and double domination of a fuzzy graph in [4]. Moreover, given any positive rational numbers a, b and cwith  there exists a fuzzy graph Gsuch that    and  where  is a total domination,  is a double domination, and  is a restrained double domination.

fuzzy graph, domination, double domination, restrained double domination, split domination, total domination.