Abstract
A one-to-one map \(\lambda \) from \(E(G) \cup V (G)\) onto the integers \(\left \{1,2,\ldots,e + v\right \}\) is a vertex-magic total labeling if there is a constant h so that for every vertex x,
where the sum is over all vertices y adjacent to x. So the magic requirement is wt(x) = h for all x. The constant h is called the magic constant for λ. Again, a graph with a vertex-magic total labeling will be called vertex-magic.
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Marr, A.M., Wallis, W.D. (2013). Vertex-Magic Total Labelings. In: Magic Graphs. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-8391-7_3
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