Geodesic
Vertex-antimagic total labelings of graphs
Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 67-83

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In this paper we introduce a new type of graph labeling for a graph G(V,E) called an (a,d)-vertex-antimagic total labeling. In this labeling we assign to the vertices and edges the consecutive integers from 1 to |V|+|E| and calculate the sum of labels at each vertex, i.e., the vertex label added to the labels on its incident edges. These sums form an arithmetical progression with initial term a and common difference d.
Keywords: super-magic labeling, (a,d)-vertex-antimagic total labeling, (a,d)-antimagic labeling 
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     title = {Vertex-antimagic total labelings of graphs},
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Bača, Martin; MacDougall, James; Bertault, François; Miller, Mirka; Simanjuntak, Rinovia; Slamin, ---. Vertex-antimagic total labelings of graphs. Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 67-83. http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a4/