The study of valuations of graphs is a relatively young part of graph theory. In this article we survey what is known about certain graph valuations, that is, labeling methods: antimagic labelings, edge-magic total labelings and vertex-magic total labelings.
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. We investigate basic properties of these labelings, show...
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