Vertex-magic labeling of regular graphs: Disjoint unions and assemblages

We establish the existence of vertex-magic total labelings (VMTLs) for several infinite classes of regular graphs. The main method of construction is to assemble a number of appropriately labeled copies of one graph into a single graph with a VMTL. This method enables us for example to begin with any even-regular graph and from it construct a cubic graph possessing a VMTL. An important feature of the construction is that it produces strong   VMTLs for many even order regular graphs. In addition the method provides another proof that for any odd-regular graph GG possessing a VMTL, the disconnected graph tGtG has a VMTL for all t≥1t≥1. The construction also extends to certain families of non-regular graphs.