  A magic labelling of a graph $G$ with magic sum $s$ is a labelling of the
edges of $G$ by nonnegative integers such that for each vertex $v\in V$, the
sum of labels of all edges incident to $v$ is equal to the same number $s$.
Stanley gave remarkable results on magic labellings, but the distinct labelling
case is much more complicated. We consider the complete construction of all
magic labellings of a given graph $G$. The idea is illustrated in detail by
dealing with three regular graphs. We give combinatorial proofs. The structure
result was used to enumerate the corresponding magic distinct labellings.
