LAUSR

A simple graph G = (V,E) admits an H-covering if every edge in E belongs to at least one subgraph of G isomorphic to a given graph H. The graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V [E ! {1, 2, . . . , |V |+|E|} such that, for all subgraphs H′ of G isomorphic to H, the H′-weights, wtf (H′) = Σ v2V (H′) f(v) + Σ e2E(H′) f(e), 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 prove the existence of super (a, d)-H-antimagic labelings of fan graphs and ladders for H isomorphic to a cycle.