Construction for antimagic generalized web graphs

An antimagic labeling of a graph with q edges is a bijection from the set of edges to the set of integers {1, 2, ..., q} such that all vertex weights are pairwise distinct, where the vertex weight is the sum of labels of all edges incident with the vertex. Let [n] = {1, 2, ..., n}. A completely separating system on [n] is a collection C of subsets of [n] in which, for each pair a ≠ b ∈ [n], there exist A,B ∈ C such that a ∈ A, b ∉ A and b ∈ B, a ∉ B. Recently, a relationship between completely separating systems and labeling of graphs has been shown to exist. Based on this relationship, antimagic labelings of various graphs have been constructed. In this paper, we extend our method to produce more general results for generalized web graphs.