Let denote the disjoint union of copies of . For each integer it is shown that the disjoint union has a strong vertex-magic total labeling (and therefore it must also have a strong edge-magic total labeling). For each integer it is shown that the disjoint union has a strong vertex-magic total labeling. These results clarify a conjecture on the magic labeling of 2-regular graphs, which posited that no such labelings existed. It is also shown that for each integer the disjoint union has a strong vertex-magic total labeling. The construction employs a technique of shifting rows of (newly constructed) Kotzig arrays to label copies of . The results add further weight to a conjecture of MacDougall regarding the existence of vertex-magic total labeling for regular graphs.