Let G(V,E) be a simple graph with m edges. For a given integer k, a k-shifted antimagic labeling is a bijection f:E(G)→{k+1,k+2,…,k+m} such that all vertices have different vertex-sums, where the vertex-sum of a vertex v is the total of the labels assigned to the edges incident to v. A graph G is {\it k-shifted antimagic} if it admits a k-shifted antimagic labeling. For the special case when k=0, a 0-shifted antimagic labeling is known as {\it antimagic labeling}; and G is {\it antimagic} if it admits an antimagic labeling. A spider is a tree with exactly one vertex of degree greater than two. A spider forest is a graph where each component is a spider. In this article, we prove that certain spider forests are k-shifted antimagic for all k≥0. In addition, we show that for a spider forest G with m edges, there exists a positive integer k0<m such that G is k-shifted antimagic for all k≥k0 and k≤−(m+k0+1).
