Solution of the conjecture: If image, image, then image has a super vertex-magic total labeling 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 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. MacDougall, Miller and Sugeng proposed the conjecture: If image, image, then image has a super vertex-magic total labeling (VMTL). We prove that this conjecture holds true by means of giving a family of super VMTLs of image, image.