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

MacDougall, James A. and Miller, Mirka and Bača, Martin (2006) Vertex-magic Total Labeling of Generalized Petersen Graphs and Convex Polytopes. Journal of Combinatorial Mathematics and Combinatorial Computing, 58 . pp. 89-99.

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A {\em 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, . . . , $v + e$ 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.