Abstract
Let G = (V, E) be a finite, simple and undirected graph. The edge-magic total or vertex-magic total labeling of G is a bijection f from V(G) ∪ E(G) onto the set of consecutive integers {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.
