Vertex-magic Total Labeling of Generalized Petersen Graphs and Convex Polytopes

A vertex-magic total labeling on a graph with \( v \) vertices and \( e \) edges is a one-to-one map taking the vertices and edges onto the integers \( 1, 2, \ldots, v+e \) with the property that the sum of the label on a vertex and the labels of its incident edges is constant, independent of the choice of vertex. We give vertex-magic total labelings for several classes of regular graphs. The paper concludes with several conjectures and open problems in the area.