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 ∖ {0 A } 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 ℤ k -antimagic and k ≥ 2} . In this paper, we determine the integer-antimagic spectra for all Hamiltonian graphs.