On total labelings of graphs with prescribed weights

Let G=(V,E)G=(V,E) be a finite, simple and undirected graph. The edge-magic total or vertex-magic total labeling of GG is a bijection ff from V(G)∪E(G)V(G)∪E(G) onto the set of consecutive integers {1,2,…,|V(G)|+|E(G)|}{1,2,…,|V(G)|+|E(G)|}, such that all the edge weights or vertex weights are equal to a constant, respectively. When all the edge weights or vertex weights are different then the labeling is called edge-antimagic or vertex-antimagic total, respectively.In this paper we provide some classes of graphs that are simultaneously super edge-magic total and super vertex-antimagic total, that is, graphs admitting labeling that has both properties at the same time. We show several results for fans, sun graphs, caterpillars and prisms.