The integer-antimagic spectra of Hamiltonian graphs

Abstract

Let A be a nontrivial abelian group. A connected simple graph G = (V, E) is A-antimagic, if there exists an edge labeling f: E(G) → A\{0A} such that the induced vertex labeling f+(v) = Σ{u,v} ∈ E(G) f({u,v}) is a one-to-one map. The integer-antimagic spectrum of a graph G is the set IAM(G) = {k: G is Zk-antimagic and k ≥ 2}. In this paper, we determine the integer-antimagic spectra for all Hamiltonian graphs.