Let \( G = (V, E) \) be a graph with order \(|G|\) and size \(|E|\). An \((a, d)\)-vertex-antimagic total labeling is a bijection \( \alpha \) from the set of all vertices and edges to the set of consecutive integers \(\{1, 2, \ldots, |V| + |E|\}\), such that the weights of the vertices form an arithmetic progression with the initial term \( a \) and the common difference \( d \). If \( \alpha(V(G)) = \{1, 2, \ldots, |V|\} \) then we call the labeling super \((a, d)\)-vertex antimagic total. In this paper, we show some basic properties of such labelings on a disjoint union of regular graphs and demonstrate how to construct such labelings for some classes of graphs, such as cycles, generalized Petersen graphs, and circulant graphs, for \( d = 1 \).