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Ladders and fan graphs are cycle-antimagic

Abstract:

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: (formula presented)such that, for∑ all subgraphs H′ of G isomorphic to H, the H′-weights, (formula presented), 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.