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Let \( G_1 \) and \( G_2 \) be any two 2-regular graphs, each with \( n \) vertices. Let \( G \) be any cubic graph obtained from \( G_1 \) and \( G_2 \) by adding \( n \) edges, each of which joins a vertex in \( G_1 \) to a vertex in \( G_2 \). We show that \( G \) has a myriad of vertex-magic total labelings, with at least three different magic constants. This class of cubic graphs includes all generalized Petersen graphs.