Two new methods to obtain super vertex-magic total labelings of graphs Original Research Article

Let image be a finite non-empty graph, where V and E are the sets of vertices and edges of G, respectively, and image and image. A vertex-magic total labeling (VMTL) is a bijection image from image to the consecutive integers image with the property that for every image, image, for some constant h. Such a labeling is super if image. In this paper, two new methods to obtain super VMTLs of graphs are put forward. The first, from a graph G with some characteristics, provides a super VMTL to the graph kG graph composed by the disjoint unions of k copies of G, for a large number of values of k. The second, from a graph image which admits a super VMTL; for instance, the graph kG, provides many super VMTLs for the graphs obtained from image by means of the addition to it of various sets of edges.