It has been shown that if the definition of a fuzzy subgraph is changed by replacing minimum with an arbitrary t-norm, then many fundamental results are no longer valid. The difference is sufficiently strong as to open an entirely new area of research in the theory and application of fuzzy graphs. In this paper, we examine how this change in definition effects various operations on fuzzy graphs. We show that some of the basic results on operations of fuzzy graphs do not hold when minimum is replaced with an arbitrary t-norm.

fuzzy graph, t-norm, Cartesian product, composition, union, join.