Let G=(V,E) be a simple graph with n vertices and m edges. A labeling of G is a bijection from the set of edges to the set {1,2,…,m} of integers, for each vertex, its vertex sum is defined to be the sum of labels of all edges incident to it. If all vertices have distinct vertex sums, we call this labeling anti-magic. Suppose f is an anti-magic labeling of G, and for any two vertices u,v with deg(u) < deg(v), if vertex sum of u is strictly less than vertex sum of v, then we say f is a strongly anti-magic labeling of G. In this thesis, we restrict our graphs to double spider graphs. Since some of double spider graphs have already been proven to be anti-magic, we will prove a stronger result here, that is, all double spider graphs are strongly anti-magic.