Vertex-magic labelings: mutations

In this paper, we are studying vertex-magic total labelings of simple graphs. We introduce a procedure called mutation which transforms one labeling into another by swapping sets of edges among vertices. The result of a mutation may be a different labeling of the same graph or a labeling of a different graph. Mutation proves to be a remarkably fruitful process—for example we are able to generate labelings for all the order 10 cubic graphs from a single initial labeling of the 5-prism. We describe all possible mutations of a labeling of the path and the cycle.