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)=∑{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.

Keywords

• hamiltonian graphs, graph labeling, group-antimagic labeling