On super vertex-antimagic total labelings of disjoint union of paths

Let G = (V,E) be a (p, q)-graph of order p and size q and f be a bijection from the set V ∪ E to the set of the first p + q natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say f is an (a, d)-vertex-antimagic total labeling if the vertex-weights form an arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study super (a, d)-vertex-antimagic total properties of disjoint union of paths.