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Let G = (V,E) be a graph with order |G| and size |E|. An (a, d)-vertexantimagic total labeling is a bijection α from all vertices and edges to the set of consecutive integers {1, 2, ..., |V | + |E|}, such that the weights of the vertices form an arithmetic progression with the initial term a and the common difference d. If α(V (G)) = {1, 2, . . . , |V |} then we call the labeling a super (a, d)-vertex antimagic total. In this paper we show how to construct such labelings for circulant graphs Cn(1, 2, 3), for d = 0, 1, 2, 3, 4, 8.

VERTEX (<I>A,D</I>)-ANTIMAGIC TOTAL LABELING ON CIRCULANT GRAPH C<SUB>N</SUB>(1,2,3)